Hovering efficiency comparison of rotary and flapping flight for a rigid and rectangular wings via dimensionless multi-objective optimization.

Science.gov (United States)

Bayiz, Yagiz Efe; Ghanaatpishe, Mohammad; Fathy, Hosam; Cheng, Bo

2018-03-20

In this work, a multi-objective optimization framework is developed for optimizing low-Reynolds number (Re) hovering flight. This framework is then applied to compare the efficiency of rigid revolving and flapping wings with rectangular shape under varying Re and Rossby number (Ro, or aspect ratio). The proposed framework is capable of generating sets of optimal solutions and Pareto fronts for maximizing lift coefficient and minimizing power coefficient in dimensionless space, which explicitly reveal the trade off between lift generation and power consumption. The results indicate that revolving wings are more efficient if the required average lift coefficient CL is low (< 1 for Re = 100 and < 1.6 for Re = 8000), while flapping wings are more efficient in achieving higher CL. Using dimensionless power loading as the single objective performance measure to be maximized, rotary flight is more efficient than flapping wings for Re > 100 regardless of the amount of energy storage assumed in the flapping-wing actuation mechanism, while flapping flight becomes more efficient for Re < 100. It is observed that wings with low Ro perform better if higher CL is needed, whereas higher Ro cases are more efficient at CL < 0.9 region. However, for the selected geometry and Re, the efficiency is weakly dependent on Ro if the dimensionless power loading is maximized. © 2018 IOP Publishing Ltd.

Comparing Jupiter and Saturn: dimensionless input rates from plasma sources within the magnetosphere

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V. M. Vasyliūnas

2008-06-01

Full Text Available The quantitative significance for a planetary magnetosphere of plasma sources associated with a moon of the planet can be assessed only by expressing the plasma mass input rate in dimensionless form, as the ratio of the actual mass input to some reference value. Traditionally, the solar wind mass flux through an area equal to the cross-section of the magnetosphere has been used. Here I identify another reference value of mass input, independent of the solar wind and constructed from planetary parameters alone, which can be shown to represent a mass input sufficiently large to prevent corotation already at the source location. The source rate from Enceladus at Saturn has been reported to be an order of magnitude smaller (in absolute numbers than that from Io at Jupiter. Both reference values, however, are also smaller at Saturn than at Jupiter, by factors ~40 to 60; expressed in dimensionless form, the estimated mass input from Enceladus may be larger than that from Io by factors ~4 to 6. The magnetosphere of Saturn may thus, despite a lower mass input in kg s⁻¹, intrinsically be more heavily mass-loaded than the magnetosphere of Jupiter.

Comparing Jupiter and Saturn: dimensionless input rates from plasma sources within the magnetosphere

Directory of Open Access Journals (Sweden)

V. M. Vasyliūnas

2008-06-01

Full Text Available The quantitative significance for a planetary magnetosphere of plasma sources associated with a moon of the planet can be assessed only by expressing the plasma mass input rate in dimensionless form, as the ratio of the actual mass input to some reference value. Traditionally, the solar wind mass flux through an area equal to the cross-section of the magnetosphere has been used. Here I identify another reference value of mass input, independent of the solar wind and constructed from planetary parameters alone, which can be shown to represent a mass input sufficiently large to prevent corotation already at the source location. The source rate from Enceladus at Saturn has been reported to be an order of magnitude smaller (in absolute numbers than that from Io at Jupiter. Both reference values, however, are also smaller at Saturn than at Jupiter, by factors ~40 to 60; expressed in dimensionless form, the estimated mass input from Enceladus may be larger than that from Io by factors ~4 to 6. The magnetosphere of Saturn may thus, despite a lower mass input in kg s−1, intrinsically be more heavily mass-loaded than the magnetosphere of Jupiter.

A noteworthy dimensionless constant in gravitation theory

International Nuclear Information System (INIS)

Fayos, F.; Lobo, J.A.; Llanta, E.

1986-01-01

A simple problem of gravitation is studied classically and in the Schwarzchild framework. A relationship is found between the parameters that define the trajectories of two particles (the first in radial motion and the second in a circular orbit) which are initially together and meet again after one revolution of particle 2. Dimensional analysis is the clue to explain the appearance of a dimensionless constant in the Newtonian case. (author)

Dimensionless Analysis for Designing Domestic Rainwater Harvesting Systems at the Regional Level in Northern Taiwan

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Chao-Hsien Liaw

2014-12-01

Full Text Available A regional-level and dimensionless analysis for designing a domestic rainwater harvesting system (DRWHS was developed. To consider various combinations of water demand, storage capacity, effective roof area, and rainfall in DRWHS design, two dimensionless ratios were used, namely, demand fraction and storage fraction, along with a relationship between the two ratios. Firstly, Northern Taiwan was divided into four sub-regions through cluster analysis based on the average annual 10-day rainfall distribution at rainfall stations and administrative districts. Easy-to-use dimensionless curves between demand fraction and storage fraction were obtained for five rainwater supply reliabilities of the DRWHS for the four sub-regions. Based on the dimensionless curves, a nomogram was constructed for designing DRWHSs at a rainwater supply reliability of 95% in the sub-region I. Storage capacities determined from the dimensionless curves showed a close fit with those determined from simulated values, but were larger than the values estimated from the method presented in the Green Building Evaluation Manual in most situations. The methodology developed herein can be used effectively for the preliminary design of a DRWHS and for overcoming the difficulties faced in designing a DRWHS without rainfall data and with incomplete rainfall data.

Error analysis of dimensionless scaling experiments with multiple points using linear regression

International Nuclear Information System (INIS)

Guercan, Oe.D.; Vermare, L.; Hennequin, P.; Bourdelle, C.

2010-01-01

A general method of error estimation in the case of multiple point dimensionless scaling experiments, using linear regression and standard error propagation, is proposed. The method reduces to the previous result of Cordey (2009 Nucl. Fusion 49 052001) in the case of a two-point scan. On the other hand, if the points follow a linear trend, it explains how the estimated error decreases as more points are added to the scan. Based on the analytical expression that is derived, it is argued that for a low number of points, adding points to the ends of the scanned range, rather than the middle, results in a smaller error estimate. (letter)

Development of Dimensionless Index Assessing Low Impact Development in Urban Areas

Science.gov (United States)

Jun, S. H.; Lee, E. H.; Kim, J. H.

2017-12-01

Because the rapid urbanization and industrialization have increased the impervious area of watersheds, inundation in urban area and water pollution of river by non-point pollutants have caused serious problems for a long time. Low Impact Development (LID) techniques have been implemented for the solution of these problems due to its cost effectiveness for mitigating the water quality and quantity impact on urban areas. There have been many studies about the effectiveness of LID, but there is a lack of research on developing an index for the assessment of LID performance. In this study, the dimensionless reliability index of LID is proposed. The index is developed using Distance Measure Method (DMM). DMM is used to consider the parameters that have different units. The parameters for reliability of LID are the amount of pollutant at the outfall and the flooding volume. Both parameters become dimensionless index by DMM. Weighted factors in dimensionless index are considered to realize the behavior of reliability for the variation of importance to the parameters. LID is applied to an actual area called Gasan city in Seoul, South Korea where inundation is frequently occurred. The reliability is estimated for 16 different rainfall events. For each rainfall event, the parameters with LID installation are compared with those of no LID installation. Depending on which parameter is considered more important, the results showed difference. In conclusion, the optimal locations of LID are suggested as the weighted factors change.

Theoretical investigation of the upper and lower bounds of a generalized dimensionless bearing health indicator

Science.gov (United States)

Wang, Dong; Tsui, Kwok-Leung

2018-01-01

Bearing-supported shafts are widely used in various machines. Due to harsh working environments, bearing performance degrades over time. To prevent unexpected bearing failures and accidents, bearing performance degradation assessment becomes an emerging topic in recent years. Bearing performance degradation assessment aims to evaluate the current health condition of a bearing through a bearing health indicator. In the past years, many signal processing and data mining based methods were proposed to construct bearing health indicators. However, the upper and lower bounds of these bearing health indicators were not theoretically calculated and they strongly depended on historical bearing data including normal and failure data. Besides, most health indicators are dimensional, which connotes that these health indicators are prone to be affected by varying operating conditions, such as varying speeds and loads. In this paper, based on the principle of squared envelope analysis, we focus on theoretical investigation of bearing performance degradation assessment in the case of additive Gaussian noises, including distribution establishment of squared envelope, construction of a generalized dimensionless bearing health indicator, and mathematical calculation of the upper and lower bounds of the generalized dimensionless bearing health indicator. Then, analyses of simulated and real bearing run to failure data are used as two case studies to illustrate how the generalized dimensionless health indicator works and demonstrate its effectiveness in bearing performance degradation assessment. Results show that squared envelope follows a noncentral chi-square distribution and the upper and lower bounds of the generalized dimensionless health indicator can be mathematically established. Moreover, the generalized dimensionless health indicator is sensitive to an incipient bearing defect in the process of bearing performance degradation.

Dimensionless parameters, scaling laws, and the implications for ETG

Energy Technology Data Exchange (ETDEWEB)

Castle, G.G.

1995-04-20

ETG will be useful in resolving several physical issues relevant to Spherical Tokamak Reactor concepts. First, it will provide a test of whether transport is Bohm or gyro-Bohm in nature. The second point is that ETG will operate in a completely different range of {rho}* space from other high performance machines, opening up a previously inaccessible region of parameter space. ETG is also a (very) high-{beta} machine. It would be the only device that would have all of its parameters except {rho}* similar to those of a Spherical tokamak Reactor. If it turns out that the transport scales definitively as either Bohm or gyro-Bohm, then extrapolation to reactor conditions with significantly lower values of {rho}* would become more credible. It is also shown that in general one cannot obtain a power law relation in the dimensionless variables for the confinement tim from a power law fit to the engineering variables. It is shown, however, that if T{sub i}/T{sub e} and n{sub i}/n{sub e} are constant or if a modified definition of certain dimensionless variables is adopted, then such a power law conversion is possible.

A dimensionless approach for the runoff peak assessment: effects of the rainfall event structure

Science.gov (United States)

Gnecco, Ilaria; Palla, Anna; La Barbera, Paolo

2018-02-01

The present paper proposes a dimensionless analytical framework to investigate the impact of the rainfall event structure on the hydrograph peak. To this end a methodology to describe the rainfall event structure is proposed based on the similarity with the depth-duration-frequency (DDF) curves. The rainfall input consists of a constant hyetograph where all the possible outcomes in the sample space of the rainfall structures can be condensed. Soil abstractions are modelled using the Soil Conservation Service method and the instantaneous unit hydrograph theory is undertaken to determine the dimensionless form of the hydrograph; the two-parameter gamma distribution is selected to test the proposed methodology. The dimensionless approach is introduced in order to implement the analytical framework to any study case (i.e. natural catchment) for which the model assumptions are valid (i.e. linear causative and time-invariant system). A set of analytical expressions are derived in the case of a constant-intensity hyetograph to assess the maximum runoff peak with respect to a given rainfall event structure irrespective of the specific catchment (such as the return period associated with the reference rainfall event). Looking at the results, the curve of the maximum values of the runoff peak reveals a local minimum point corresponding to the design hyetograph derived according to the statistical DDF curve. A specific catchment application is discussed in order to point out the dimensionless procedure implications and to provide some numerical examples of the rainfall structures with respect to observed rainfall events; finally their effects on the hydrograph peak are examined.

Can we calculate the fundamental dimensionless constants of physics

International Nuclear Information System (INIS)

Barut, A.O.

1987-07-01

We review some dynamical models to calculate the dimensionless constants α=e 2 /4πε 0 (h/2π)c, β=M p /m e (or β'=m μ /m e ), γ=G Fermi m e 2 /c(h/2π) 3 and δ=G Newton m e 2 /(e 2 /4πε 0 ) which are associated with the four different manifestations (electromagnetic, strong, weak and gravitational) of a possible single interaction. (author). 15 refs

Dimensionless Energy Conversion Characteristics of an Air-Powered Hydraulic Vehicle

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Dongkai Shen

2018-02-01

Full Text Available Due to the advantages of resource conservation and less exhaust emissions, compressed air-powered vehicle has attracted more and more attention. To improve the power and efficiency of air-powered vehicle, an air-powered hydraulic vehicle was proposed. As the main part of the air-powered hydraulic vehicles, HP transformer (short for Hydropneumatic transformer is used to convert the pneumatic power to higher hydraulic power. In this study, to illustrate the energy conversion characteristics of air-powered hydraulic vehicle, dimensionless mathematical model of the vehicle’s working process was set up. Through experimental study on the vehicle, the dimensionless model was verified. Through simulation study on the vehicle, the following can be obtained: firstly, the increase of the hydraulic chamber orifice and the area ratio of the pistons can lead to a higher output power, while output pressure is just the opposite. Moreover, the increase of the output pressure and the aperture of the hydraulic chamber can lead to a higher efficiency, while area ratio of the pistons played the opposite role. This research can be referred to in the performance and design optimization of the HP transformers.

A Diagnosis Method for Rotation Machinery Faults Based on Dimensionless Indexes Combined with K-Nearest Neighbor Algorithm

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Jianbin Xiong

2015-01-01

Full Text Available It is difficult to well distinguish the dimensionless indexes between normal petrochemical rotating machinery equipment and those with complex faults. When the conflict of evidence is too big, it will result in uncertainty of diagnosis. This paper presents a diagnosis method for rotation machinery fault based on dimensionless indexes combined with K-nearest neighbor (KNN algorithm. This method uses a KNN algorithm and an evidence fusion theoretical formula to process fuzzy data, incomplete data, and accurate data. This method can transfer the signals from the petrochemical rotating machinery sensors to the reliability manners using dimensionless indexes and KNN algorithm. The input information is further integrated by an evidence synthesis formula to get the final data. The type of fault will be decided based on these data. The experimental results show that the proposed method can integrate data to provide a more reliable and reasonable result, thereby reducing the decision risk.

Stoichiometric network analysis and associated dimensionless kinetic equations. Application to a model of the Bray-Liebhafsky reaction.

Science.gov (United States)

Schmitz, Guy; Kolar-Anić, Ljiljana Z; Anić, Slobodan R; Cupić, Zeljko D

2008-12-25

The stoichiometric network analysis (SNA) introduced by B. L. Clarke is applied to a simplified model of the complex oscillating Bray-Liebhafsky reaction under batch conditions, which was not examined by this method earlier. This powerful method for the analysis of steady-states stability is also used to transform the classical differential equations into dimensionless equations. This transformation is easy and leads to a form of the equations combining the advantages of classical dimensionless equations with the advantages of the SNA. The used dimensionless parameters have orders of magnitude given by the experimental information about concentrations and currents. This simplifies greatly the study of the slow manifold and shows which parameters are essential for controlling its shape and consequently have an important influence on the trajectories. The effectiveness of these equations is illustrated on two examples: the study of the bifurcations points and a simple sensitivity analysis, different from the classical one, more based on the chemistry of the studied system.

Dimensionless groups for multidimensional heat and mass transfer in adsorbed natural gas storage

Energy Technology Data Exchange (ETDEWEB)

Sphaier, L.A. [Universidade Federal Fluminense (UFF), Niteroi, RJ (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica. Lab. de Mecanica Teorica e Aplicada], E-mail: lasphaier@mec.uff.br

2010-07-01

This paper provides a new methodology for analyzing heat and mass transfer in gas storage via adsorption. The foundation behind the proposed methodology comprises a set of physically meaningful dimensionless groups. A discussion regarding the development of such groups is herein presented, providing a fully normalized multidimensional formulation for describing the transport mechanisms involved in adsorbed gas storage. After such presentation, data from previous literature studies associated with the problem of adsorbed natural gas storage are employed for determining realistic values for the developed parameters. Then, a one-dimensional test-case problem is selected for illustrating the application of the dimensionless formulation for simulating the operation of adsorbed gas reservoirs. The test problem is focused on analyzing an adsorbed gas discharge operation. This problem is numerically solved, and the solution is verified against previously published literature data. The presented results demonstrate how a higher heat of sorption values lead to reduced discharge capacities. (author)

Mass-Inertial Characteristics and Dimensionless Equations of Two-bearing Rotor Motion with Auto-balancer in Terms of Compensating Body Mass

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A. N. Gorbenko

2015-01-01

Full Text Available Modern rotary machines use auto-balancing devices of passive type to provide automatic balancing of rotors and reduce vibration. Most available researches on the rotor auto-balancing dynamics and stability are based on the assumption that the compensating bodies of the autobalancer, as well as the rotor imbalance, are infinitesimal values. The literature review has shown that the problems concerning the automatic balancing of rotor with its three-dimensional motion are solved approximately and require an in-depth analysis taking into consideration the final mass of the compensating bodies.The paper analyses the effect of an auto-balancer mass on the mass-inertial properties of the three-dimensional rotor motion. It gives the autonomous equations of the system motion. The work shows that attaching the point masses of compensating auto-balancer bodies and imbalance to the rotor causes an increase, however non-identical, in all components of the total inertia tensor of the mechanical system. This leads to a qualitative change in mass-inertial characteristics of the system.The composite rotor becomes an inertia anisotropic body in which the inertia moments about the two transverse own axes are not equal to each other. The rotor anisotropy results in complicated dynamic behavior of the gyroscopic rotor. In this case, the additional critical rotor speeds and the zones of instability of motion may occur.It is shown that in the case of using multi-body auto-balancer the inertial parameters of the rotor system grow into the interval values, i.e. their values are not uniquely determined and may be equal to a variety values from a certain range. Thus, the degree of inertial anisotropy and other auto-balancing parameters are the interval values as well in this case.The system of dimensionless equations of rotary machine motion, which contains the minimum required number of dimensionless parameters, has been obtained. The specific ranges of the dimensionless

Wear numbers for ball cup and journal bearings

NARCIS (Netherlands)

Ligterink, D.J.; Moes, H.

1980-01-01

A wear number is defined for ball cup bearings and for journal bearings where the cup and the cylindrical bearing are made of soft material. This dimensionless wear number provides a relation between the following five quantities: the radius of the ball or the length of the journal bearing in

Technical characterization of dialysis fluid flow and mass transfer rate in dialyzers with various filtration coefficients using dimensionless correlation equation.

Science.gov (United States)

Fukuda, Makoto; Yoshimura, Kengo; Namekawa, Koki; Sakai, Kiyotaka

2017-06-01

The objective of the present study is to evaluate the effect of filtration coefficient and internal filtration on dialysis fluid flow and mass transfer coefficient in dialyzers using dimensionless mass transfer correlation equations. Aqueous solution of vitamin B 12 clearances were obtained for REXEED-15L as a low flux dialyzer, and APS-15EA and APS-15UA as high flux dialyzers. All the other design specifications were identical for these dialyzers except for filtration coefficient. The overall mass transfer coefficient was calculated, moreover, the exponents of Reynolds number (Re) and film mass transfer coefficient of the dialysis-side fluid (k D ) for each flow rate were derived from the Wilson plot and dimensionless correlation equation. The exponents of Re were 0.4 for the low flux dialyzer whereas 0.5 for the high flux dialyzers. Dialysis fluid of the low flux dialyzer was close to laminar flow because of its low filtration coefficient. On the other hand, dialysis fluid of the high flux dialyzers was assumed to be orthogonal flow. Higher filtration coefficient was associated with higher k D influenced by mass transfer rate through diffusion and internal filtration. Higher filtration coefficient of dialyzers and internal filtration affect orthogonal flow of dialysis fluid.

Reynolds number and friction coefficient for axial-parallel flow through complex cross-sections

International Nuclear Information System (INIS)

Markfort, D.

1975-01-01

Thermal and hydraulic lay-out of reactor fuel elements and other heat transfer equipment makes use of established functional relationship between dimensionless characters, the former being transferred from circular tube to more complex geometries. The stringent requirement (from theory) for 'geometrical similarity' is bypassed by defining 'equivalent diameters'. But dimensionless numbers may be derived from 'flow-integral-conditions' while the geometrical components contained therein reduce if not completely abolish the requirement for geometrical similarity. The derivation is demonstrated by using the Reynolds number. A friction coefficient valid for any kind of flow regime can be defined using integral-conditions. Correlations of friction coefficient and Reynolds number using universal-velocity profiles confirm the analysis when compared to well known experimental data. (orig.) [de

Scaling up adsorption media reactors for copper removal with the aid of dimensionless numbers.

Science.gov (United States)

Chang, Ni-Bin; Houmann, Cameron; Wanielista, Martin

2016-02-01

Adsorption media may be used to sorb copper in an aquatic environment for pollution control. Effective design of adsorption media reactors is highly dependent on selection of the hydraulic residence time when scaling up a pilot-scale reactor to a field-scale reactor. This paper seeks to improve scaling-up technique of the reactor design process through the use of the Damköhler and Péclet numbers via a dimensional analysis. A new scaling-up theory is developed in this study through a joint consideration of the Damköhler and Péclet numbers for a constant media particle size such that a balance between transport control and reaction control can be harmonized. A series of column breakthrough tests at varying hydraulic residence times revealed a clear peak adsorption capacity at a Damköhler number of 2.74. The Péclet numbers for the column breakthrough tests indicated that mechanical dispersion is an important effect that requires further consideration in the scaling-up process. However, perfect similitude of the Damköhler number cannot be maintained for a constant media particle size, and relaxation of hydrodynamic similitude through variation of the Péclet number must occur. Copyright © 2015 Elsevier Ltd. All rights reserved.

Crossover from High to Low Reynolds Number Turbulence

NARCIS (Netherlands)

Lohse, Detlef

1994-01-01

The Taylor-Reynolds and Reynolds number (Re lambda and Re) dependence of the dimensionless energy dissipation rate c epsilon = epsilon L / u31,rms is derived for statistically stationary isotropic turbulence, employing the results of a variable range mean field theory. Here epsilon is the energy

Effects of soil-structure in high-rise buildings by means of dimensionless analysis and a simplified model

NARCIS (Netherlands)

Gómez, S.S.; Pruiksma, J.

2017-01-01

In this paper simplified expressions for assessing fundamental frequency and modal damping of high-rise buildings taking into account the soil-structure interaction (SSI) are proposed. To this end, several steps have been followed. First, a 3DoF model is formulated making use of dimensionless

Effect of Brinkman number and magnetic field on laminar convection ...

African Journals Online (AJOL)

The effect of Brinkman number and magnetic field on laminar convection in a vertical plate channel with uniform and asymmetric temperatures has been studied. The dimensionless form of momentum and energy balanced equations has been solved using one term perturbation series solution. The solution of the ...

Multi-objective optimization and design for free piston Stirling engines based on the dimensionless power

Science.gov (United States)

Mou, Jian; Hong, Guotong

2017-02-01

In this paper, the dimensionless power is used to optimize the free piston Stirling engines (FPSE). The dimensionless power is defined as a ratio of the heat power loss and the output work. The heat power losses include the losses of expansion space, heater, regenerator, cooler and the compression space and every kind of the heat loss calculated by empirical formula. The output work is calculated by the adiabatic model. The results show that 82.66% of the losses come from the expansion space and 54.59% heat losses of expansion space come from the shuttle loss. At different pressure the optimum bore-stroke ratio, heat source temperature, phase angle and the frequency have different values, the optimum phase angles increase with the increase of pressure, but optimum frequencies drop with the increase of pressure. However, no matter what the heat source temperature, initial pressure and frequency are, the optimum ratios of piston stroke and displacer stroke all about 0.8. The three-dimensional diagram is used to analyse Stirling engine. From the three-dimensional diagram the optimum phase angle, frequency and heat source temperature can be acquired at the same time. This study offers some guides for the design and optimization of FPSEs.

Similarity Theory and Dimensionless Numbers in Heat Transfer

Science.gov (United States)

Marin, E.; Calderon, A.; Delgado-Vasallo, O.

2009-01-01

We present basic concepts underlying the so-called similarity theory that in our opinion should be explained in basic undergraduate general physics courses when dealing with heat transport problems, in particular with those involving natural or free convection. A simple example is described that can be useful in showing a criterion for neglecting…

The H-mode pedestal, ELMs and TF ripple effects in JT-60U/JET dimensionless identity experiments

International Nuclear Information System (INIS)

Saibene, G.; Oyama, N.; Loennroth, J.; Andrew, Y.; Luna, E. de la; Giroud, C.; Huysmans, G.T.A.; Kamada, Y.; Kempenaars, M.A.H.; Loarte, A.; Donald, D. Mc; Nave, M.M.F.; Meiggs, A.; Parail, V.; Sartori, R.; Sharapov, S.; Stober, J.; Suzuki, T.; Takechi, M.; Toi, K.; Urano, H.

2007-01-01

This paper summarizes results of dimensionless identity experiments in JT-60U and JET, aimed at the comparison of the H-mode pedestal and ELM behaviour in the two devices. Given their similar size, dimensionless matched plasmas are also similar in their dimensional parameters (in particular, the plasma minor radius a is the same in JET and JT-60U). Power and density scans were carried out at two values of I p , providing a q scan (q 95 = 3.1 and 5.1) with fixed (and matched) toroidal field. Contrary to initial expectations, a dimensionless match between the two devices was quite difficult to achieve. In general, p ped in JT-60U is lower than in JET and, at low q, the pedestal pressure of JT-60U with a Type I ELMy edge is matched in JET only in the Type III ELM regime. At q 95 = 5.1, a dimensionless match in ρ*, ν* and β p,ped is obtained with Type I ELMs, but only with low power JET H-modes. These results motivated a closer investigation of experimental conditions in the two devices, to identify possible 'hidden' physics that prevents obtaining a good match of pedestal values over a large range of plasmas parameters. Ripple-induced ion losses of the medium bore plasma used in JT-60U for the similarity experiments are identified as the main difference with JET. The magnitude of the JT-60U ripple losses is sufficient to induce counter-toroidal rotation in co-injected plasma. The influence of ripple losses was demonstrated at q 95 = 5.1: reducing ripple losses by ∼2 (from 4.3 to 1.9 MW) by replacing positive with negative neutral beam injection at approximately constant P in resulted in an increased p ped in JT-60U, providing a good match to full power JET H-modes. At the same time, the counter-toroidal rotation decreased. Physics mechanisms relating ripple losses to pedestal performance are not yet identified, and the possible role of velocity shear in the pedestal stability, as well as the possible influence of ripple on thermal ion transport are briefly

Relativistic theory of tidal Love numbers

International Nuclear Information System (INIS)

Binnington, Taylor; Poisson, Eric

2009-01-01

In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.

A dimensionless criterion for characterising internal transport barriers in tokamaks

International Nuclear Information System (INIS)

Tresset, G.; Litaudon, X.; Moreau, D.

2000-07-01

A simple criterion, based on a dimensionless parameter (ρ T * =ρ s /L T ) related to drift wave turbulence stabilisation and anomalous transport theory, is proposed in order to characterise the emergence and the space-time evolution of internal transport barriers (ITB's) during a tokamak discharge. The underlying physics which led us to consider the possible relevance of this parameter as a local indicator of a bifurcated plasma state is the breaking of the gyro-Bohm turbulence scaling by the diamagnetic velocity shear, which has been observed in various numerical simulations [e.g. X. Garbet and R.E. Waltz, Phys. Plasmas 3(1996) 1898]. The presence of an ITB is inferred when ρ T * exceeds a threshold value. The main features like the emergence time, location and even dynamics of ITB's can then be summarized on a single graphical representation consistent with measurement uncertainties. The validity of such a criterion is demonstrated on the Optimized Shear (OS) database of JET in several experimental configurations. Large database analysis and realtime control of OS discharges are envisaged as the most attractive applications. (author)

Study of Nonlinear MHD Tribological Squeeze Film at Generalized Magnetic Reynolds Numbers Using DTM.

Science.gov (United States)

Rashidi, Mohammad Mehdi; Freidoonimehr, Navid; Momoniat, Ebrahim; Rostami, Behnam

2015-01-01

In the current article, a combination of the differential transform method (DTM) and Padé approximation method are implemented to solve a system of nonlinear differential equations modelling the flow of a Newtonian magnetic lubricant squeeze film with magnetic induction effects incorporated. Solutions for the transformed radial and tangential momentum as well as solutions for the radial and tangential induced magnetic field conservation equations are determined. The DTM-Padé combined method is observed to demonstrate excellent convergence, stability and versatility in simulating the magnetic squeeze film problem. The effects of involved parameters, i.e. squeeze Reynolds number (N1), dimensionless axial magnetic force strength parameter (N2), dimensionless tangential magnetic force strength parameter (N3), and magnetic Reynolds number (Rem) are illustrated graphically and discussed in detail. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems and biological prosthetics.

Study of Nonlinear MHD Tribological Squeeze Film at Generalized Magnetic Reynolds Numbers Using DTM.

Directory of Open Access Journals (Sweden)

Mohammad Mehdi Rashidi

Full Text Available In the current article, a combination of the differential transform method (DTM and Padé approximation method are implemented to solve a system of nonlinear differential equations modelling the flow of a Newtonian magnetic lubricant squeeze film with magnetic induction effects incorporated. Solutions for the transformed radial and tangential momentum as well as solutions for the radial and tangential induced magnetic field conservation equations are determined. The DTM-Padé combined method is observed to demonstrate excellent convergence, stability and versatility in simulating the magnetic squeeze film problem. The effects of involved parameters, i.e. squeeze Reynolds number (N1, dimensionless axial magnetic force strength parameter (N2, dimensionless tangential magnetic force strength parameter (N3, and magnetic Reynolds number (Rem are illustrated graphically and discussed in detail. Applications of the study include automotive magneto-rheological shock absorbers, novel aircraft landing gear systems and biological prosthetics.

Unravelling abiotic and biotic controls on the seasonal water balance using data-driven dimensionless diagnostics

Directory of Open Access Journals (Sweden)

S. P. Seibert

2017-06-01

Full Text Available The baffling diversity of runoff generation processes, alongside our sketchy understanding of how physiographic characteristics control fundamental hydrological functions of water collection, storage, and release, continue to pose major research challenges in catchment hydrology. Here, we propose innovative data-driven diagnostic signatures for overcoming the prevailing status quo in catchment inter-comparison. More specifically, we present dimensionless double mass curves (dDMC which allow inference of information on runoff generation and the water balance at the seasonal and annual timescales. By separating the vegetation and winter periods, dDMC furthermore provide information on the role of biotic and abiotic controls in seasonal runoff formation. A key aspect we address in this paper is the derivation of dimensionless expressions of fluxes which ensure the comparability of the signatures in space and time. We achieve this by using the limiting factors of a hydrological process as a scaling reference. We show that different references result in different diagnostics. As such we define two kinds of dDMC which allow us to derive seasonal runoff coefficients and to characterize dimensionless streamflow release as a function of the potential renewal rate of the soil storage. We expect these signatures for storage controlled seasonal runoff formation to remain invariant, as long as the ratios of release over supply and supply over storage capacity develop similarly in different catchments. We test the proposed methods by applying them to an operational data set comprising 22 catchments (12–166 km2 from different environments in southern Germany and hydrometeorological data from 4 hydrological years. The diagnostics are used to compare the sites and to reveal the dominant controls on runoff formation. The key findings are that dDMC are meaningful signatures for catchment runoff formation at the seasonal to annual scale and that the type of

Experimental constraints on transport from dimensionless parameter scaling studies

International Nuclear Information System (INIS)

Petty, C.C.; Luce, T.C.; Baker, D.R.

1998-02-01

The scalings of heat transport with safety factor (q), normalized collisionality (v), plasma beta (β), and relative gyroradius (ρ*) have been measured on the DIII-D tokamak. The measured ρ* β and v scalings of heat transport indicate that E x B transport from drive wave turbulence is a plausible basis for anomalous transport. For high confinement (H) mode plasmas where the safety factor was varied at fixed magnetic shear, the effective (or one-fluid) thermal diffusivity was found to scale like χ eff ∝ q 2.3±0.64 , with the ion and electron fluids having the same q scaling to within the experimental errors except near the plasma edge. The scaling of the thermal confinement time with safety factor was in good agreement with this local transport dependence, τ th ∝ q -2.42±0.31 ; however, when the magnetic shear was allowed to vary to keep q 0 fixed during the (edge) safety factor scan, a weaker global dependence was observed, τ th ∝ q 95 -1.43±0.23 . This weaker dependence was mainly due to the change in the local value of q between the two types of scans. The combined ρ*, β, v and q scalings of heat transport for H-mode plasmas on DIII-D reproduce the empirical confinement scaling using physical (dimensionless) parameters with the exception of weaker power degradation

THE DIMENSIONLESS AGE OF THE UNIVERSE: A RIDDLE FOR OUR TIME

Energy Technology Data Exchange (ETDEWEB)

Avelino, Arturo; Kirshner, Robert P., E-mail: aavelino@cfa.harvard.edu [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts, 02138 (United States)

2016-09-01

We present the interesting coincidence of cosmology and astrophysics that points toward a dimensionless age of the Universe H {sub 0} t {sub 0} that is close to one. Despite cosmic deceleration for 9 Gyr and acceleration since then, we find H {sub 0} t {sub 0} = 0.96 ± 0.01 for the ΛCDM model that fits SN Ia data from Pan-STARRS, CMB power spectra, and baryon acoustic oscillations. Similarly, astrophysical measures of stellar ages and the Hubble constant derived from redshifts and distances point to H {sub 0} t ∼ 1.0 ± 0.1. The wide range of possible values for H {sub 0} t {sub 0} realized during cosmic evolution means that we live at what appears to be a special time. This “synchronicity problem” is not precisely the same as the usual coincidence problem , because there are combinations of Ω{sub M} and Ω{sub Λ} for which the usual coincidence problem holds but for which H {sub 0} t {sub 0} is not close to 1.

Dictionary of scientific units including dimensionless numbers and scales

National Research Council Canada - National Science Library

Jerrard, H.G; McNeill, D.B

1992-01-01

.... The text includes the most recently accepted values of all units. Several disciplines, which have in the past employed few scientific principles and the dictionary has been extended to include examples of these.

On the number of light rings in curved spacetimes of ultra-compact objects

Science.gov (United States)

Hod, Shahar

2018-01-01

In a very interesting paper, Cunha, Berti, and Herdeiro have recently claimed that ultra-compact objects, self-gravitating horizonless solutions of the Einstein field equations which have a light ring, must possess at least two (and, in general, an even number of) light rings, of which the inner one is stable. In the present compact paper we explicitly prove that, while this intriguing theorem is generally true, there is an important exception in the presence of degenerate light rings which, in the spherically symmetric static case, are characterized by the simple dimensionless relation 8 πrγ2 (ρ +pT) = 1 [here rγ is the radius of the light ring and { ρ ,pT } are respectively the energy density and tangential pressure of the matter fields]. Ultra-compact objects which belong to this unique family can have an odd number of light rings. As a concrete example, we show that spherically symmetric constant density stars with dimensionless compactness M / R = 1 / 3 possess only one light ring which, interestingly, is shown to be unstable.

Dimensionless scalings of confinement, heat transport and pedestal stability in JET-ILW and comparison with JET-C

Czech Academy of Sciences Publication Activity Database

Frassinetti, L.; Saarelma, S.; Lomas, P.; Nunes, I.; Rimini, F.; Beurskens, M.N.A.; Bílková, Petra; Boom, J.E.; De La Luna, E.; Delabie, E.; Drewelow, P.; Flanagan, J.; Garzotti, L.; Giroud, C.; Hawks, N.; Joffrin, E.; Kempenaars, M.; Kim, H.-T.; Kruezi, U.; Loarte, A.; Lomanowski, B.; Lupelli, I.; Meneses, L.; Maggi, C.F.; Menmuir, S.; Peterka, Matěj; Rachlew, E.; Romanelli, M.; Stefanikova, E.

2017-01-01

Roč. 59, č. 1 (2017), č. článku 014014. ISSN 0741-3335. [EPS 2016: Conference on Plasma Physics/43./. Leuven, 04.07.2016-08.07.2016] EU Projects: European Commission(XE) 633053 - EUROfusion Institutional support: RVO:61389021 Keywords : JET-ILW * dimensionless scaling * pedestal * confinement * pedestal stability * heat transport Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 2.392, year: 2016 http://dx.doi.org/10.1088/0741-3335/59/1/014014

Dimensionless parameterization of lidar for laser remote sensing of the atmosphere and its application to systems with SiPM and PMT detectors.

Science.gov (United States)

Agishev, Ravil; Comerón, Adolfo; Rodriguez, Alejandro; Sicard, Michaël

2014-05-20

In this paper, we show a renewed approach to the generalized methodology for atmospheric lidar assessment, which uses the dimensionless parameterization as a core component. It is based on a series of our previous works where the problem of universal parameterization over many lidar technologies were described and analyzed from different points of view. The modernized dimensionless parameterization concept applied to relatively new silicon photomultiplier detectors (SiPMs) and traditional photomultiplier (PMT) detectors for remote-sensing instruments allowed predicting the lidar receiver performance with sky background available. The renewed approach can be widely used to evaluate a broad range of lidar system capabilities for a variety of lidar remote-sensing applications as well as to serve as a basis for selection of appropriate lidar system parameters for a specific application. Such a modernized methodology provides a generalized, uniform, and objective approach for evaluation of a broad range of lidar types and systems (aerosol, Raman, DIAL) operating on different targets (backscatter or topographic) and under intense sky background conditions. It can be used within the lidar community to compare different lidar instruments.

Dimensionless model to determine spontaneous combustion danger zone in the longwall gob

Institute of Scientific and Technical Information of China (English)

ZHANG Xin-hai; DENG Jun; WEN Hu

2011-01-01

According to spontaneous combustion propensity,the longwall gob is divided into three zones,including heat dissipation zone,self-heating zone and the choking zone.Only in the self-heating zone can temperature of coal rise due to oxidation.Studying the distribution of the “Three Zones” in gob is important for predicting and preventing spontaneous combustion in coalmine.In normal mining operations,temperature of coal is roughly constant.The process of mass transfer in the gob is considered to be steady.Based on mass conservation,gas species conservation,darcy' s law,Ficks law of diffusion and coal oxidation 1-grade reaction rule,governing equation for air leakage intensity and species concentration are deduced.With critical value of coal spontaneous combustion and the size of longwall workface as basic dimension,a dimensionless steady coupled model of air flow diffusion and chemical reaction in loose coal of Fully Mechanized Top-Coal Caving Mining Workface (FMTCCMW) is setup.By solving the model numerically,regulation of three zones' distribution and spontaneous combustion in the gob can be obtained.The results can be easily popularized to prediction of spontaneous combustion in other coalmines' longwall gob.

Identifying a Superfluid Reynolds Number via Dynamical Similarity.

Science.gov (United States)

Reeves, M T; Billam, T P; Anderson, B P; Bradley, A S

2015-04-17

The Reynolds number provides a characterization of the transition to turbulent flow, with wide application in classical fluid dynamics. Identifying such a parameter in superfluid systems is challenging due to their fundamentally inviscid nature. Performing a systematic study of superfluid cylinder wakes in two dimensions, we observe dynamical similarity of the frequency of vortex shedding by a cylindrical obstacle. The universality of the turbulent wake dynamics is revealed by expressing shedding frequencies in terms of an appropriately defined superfluid Reynolds number, Re(s), that accounts for the breakdown of superfluid flow through quantum vortex shedding. For large obstacles, the dimensionless shedding frequency exhibits a universal form that is well-fitted by a classical empirical relation. In this regime the transition to turbulence occurs at Re(s)≈0.7, irrespective of obstacle width.

Burnout correlations for even- and odd-numbered peripheral rod clusters over low pressure range

International Nuclear Information System (INIS)

Akaho, E.H.K.

1995-01-01

Burnout data with low pressure Freon-113 for even- and odd- numbered peripheral rod clusters with relatively large spacings were used to derive equations in terms of dimensionless parameters suggested by Barnett. The equations which are for three different flow regimes for each rod geometry (even or odd) were found to predict burnout data with maximum RMS deviation being 3.8%. (author). 11 figs., 3 tabs., 15 refs

Dimensionless Numerical Approaches for the Performance Prediction of Marine Waterjet Propulsion Units

Directory of Open Access Journals (Sweden)

Marco Altosole

2012-01-01

Full Text Available One of the key issues at early design stage of a high-speed craft is the selection and the performance prediction of the propulsion system because at this stage only few information about the vessel are available. The objective of this work is precisely to provide the designer, in the case of waterjet propelled craft, with a simple and reliable calculation tool, able to predict the waterjet working points in design and off-design conditions, allowing to investigate several propulsive options during the ship design process. In the paper two original dimensionless numerical procedures, one referred to jet units for naval applications and the other more suitable for planing boats, are presented. The first procedure is based on a generalized performance map for mixed flow pumps, derived from the analysis of several waterjet pumps by applying similitude principles of the hydraulic machines. The second approach, validated by some comparisons with current waterjet installations, is based on a complete physical approach, from which a set of non-dimensional waterjet characteristics has been drawn by the authors. The presented application examples show the validity and the degree of accuracy of the proposed methodologies for the performance evaluation of waterjet propulsion systems.

Rayleigh- and Prandtl-number dependence of the large-scale flow-structure in weakly-rotating turbulent thermal convection

Science.gov (United States)

Weiss, Stephan; Wei, Ping; Ahlers, Guenter

2015-11-01

Turbulent thermal convection under rotation shows a remarkable variety of different flow states. The Nusselt number (Nu) at slow rotation rates (expressed as the dimensionless inverse Rossby number 1/Ro), for example, is not a monotonic function of 1/Ro. Different 1/Ro-ranges can be observed with different slopes ∂Nu / ∂ (1 / Ro) . Some of these ranges are connected by sharp transitions where ∂Nu / ∂ (1 / Ro) changes discontinuously. We investigate different regimes in cylindrical samples of aspect ratio Γ = 1 by measuring temperatures at the sidewall of the sample for various Prandtl numbers in the range 3 Deutsche Forschungsgemeinschaft.

Hydrologic classification of rivers based on cluster analysis of dimensionless hydrologic signatures: Applications for environmental instream flows

Science.gov (United States)

Praskievicz, S. J.; Luo, C.

2017-12-01

Classification of rivers is useful for a variety of purposes, such as generating and testing hypotheses about watershed controls on hydrology, predicting hydrologic variables for ungaged rivers, and setting goals for river management. In this research, we present a bottom-up (based on machine learning) river classification designed to investigate the underlying physical processes governing rivers' hydrologic regimes. The classification was developed for the entire state of Alabama, based on 248 United States Geological Survey (USGS) stream gages that met criteria for length and completeness of records. Five dimensionless hydrologic signatures were derived for each gage: slope of the flow duration curve (indicator of flow variability), baseflow index (ratio of baseflow to average streamflow), rising limb density (number of rising limbs per unit time), runoff ratio (ratio of long-term average streamflow to long-term average precipitation), and streamflow elasticity (sensitivity of streamflow to precipitation). We used a Bayesian clustering algorithm to classify the gages, based on the five hydrologic signatures, into distinct hydrologic regimes. We then used classification and regression trees (CART) to predict each gaged river's membership in different hydrologic regimes based on climatic and watershed variables. Using existing geospatial data, we applied the CART analysis to classify ungaged streams in Alabama, with the National Hydrography Dataset Plus (NHDPlus) catchment (average area 3 km2) as the unit of classification. The results of the classification can be used for meeting management and conservation objectives in Alabama, such as developing statewide standards for environmental instream flows. Such hydrologic classification approaches are promising for contributing to process-based understanding of river systems.

Experimental determination of the dimensionless scaling parameter of energy transport in tokamaks

International Nuclear Information System (INIS)

Luce, T.C.; Petty, C.C.

1995-07-01

Controlled fusion experiments have focused on the variation of the plasma characteristics as the engineering or control parameters are systematically changed. This has led to the development of extrapolation formulae for prediction of future device performance using these same variables as a basis. Recently, it was noticed that present-day tokamaks can operate with all of the dimensionless variables which appear in the Vlasov-Maxwell system of equations at values projected for a fusion powerplant with the exception of the parameter ρ * , the gyroradius normalized to the machine size. The scaling with this parameter is related to the benefit of increasing the size of the machine either directly or effectively by increasing the magnetic field. It is exactly this scaling which is subject to systematic error in the inter-machine databases and the cost driver for any future machine. If this scaling can be fixed by a series of single machine experiments, much as the current and power scalings have been, the confidence in the prediction of future device performance would be greatly enhanced. While carrying out experiments of this type, it was also found that the ρ * scaling can illuminate the underlying physics of energy transport. Conclusions drawn from experiments on the DIII-D tokamak in these two areas are the subject of this paper

Simultaneous release of diclofenac sodium and papaverine hydrochloride from tablets and pellets using the flow-through cell apparatus described by dimensionless equations.

Science.gov (United States)

Kasperek, Regina

2011-01-01

The release of diclofenac sodium and papaverine hydrochloride from tablets and pellets using the flow-through cell apparatus was studied. The influence of excipients and of a size of the solid dosage forms on the amount of the released substances at the intervals of time using the different rates of flow of the dissolution medium was investigated. Physical parameters corresponding to the dissolution process as the mass transfer coefficient, the thickness of the boundary diffusion layer and the concentration of the saturated solution at this layer were calculated. The results of release were described by dimensionless equations.

Mass transfer in wetted-wall columns: correlations at high Reynolds numbers

DEFF Research Database (Denmark)

Nielsen, Christian H.E.; Kiil, Søren; Thomsen, Henrik W.

1998-01-01

(G)) were determined. In dimensionless form, the correlations are given by Sh(L) = 0.01613 Re-G(0.664) Re-L(0.426) Sc-L(0.5) Sh(G) = 0.00031 Re-G(1.05) Re-L(0.207) Sc-G(0.5) and are valid at gas-phase Reynolds numbers from 7500 to 18,300 and liquid-phase Reynolds numbers from 4000 to 12,000, conditions...... of industrial relevance. To our knowledge, no correlations for Sh(G) have been reported in the literature which are valid at such high Reynolds numbers. The wetted-wall column was equipped with six intermediate measuring positions for gas and two for liquid samples, giving rise to a high accuracy...... of the obtained correlations. Our data showed that Sh(L) and Sh(G) both depend on Re-G and Re-L due to changes in the interfacial area at the high Reynolds numbers employed. The presence of inert particles in the liquid-phase may influence the rate of mass transport, and experimental work was initiated to study...

Irreversibility analysis of non isothermal flat plate solar collectors for air heating with a dimensionless model; Analisis de las irreversibilidades en colectores solares de placas planas no isotermicos para calentamiento de aire utilizando un modelo adimensional

Energy Technology Data Exchange (ETDEWEB)

Bracamonte-Baran, Johane Hans; Baritto-Loreto, Miguel Leonardo [Universidad Central de Venezuela (Venezuela)]. E-mails: johanehb@gmail.com; johane.bracamonte@ucv.ve; miguel.baritto@ucv.ve

2013-04-15

The dimensionless model developed and validated by Baritto and Bracamonte (2012) for the thermal behavior of flat plate solar collector without glass cover is improved by adding the entropy balance equation in a dimensionless form. The model is solved for a wide range of aspect ratios and mass flow numbers. A parametric study is developed and the distribution of internal irreversibilities along the collector is analyzed. The influence of the design parameters on the entropy generation by fluid friction and heat transfer is analyzed and it is found that for certain combinations of these parameters optimal thermodynamic operation can be achieved. [Spanish] En el presente trabajo, el modelo adimensional desarrollado y validado por Baritto y Bracamonte (2012) para describir el comportamiento termico de colectores solares de placas planas sin cubierta transparente, se complementa con la ecuacion adimensional de balance de entropia para un elemento diferencial de colector solar. El modelo se resuelve para un amplio rango de valores de relaciones de aspecto y numero de flujo de masa. A partir de los resultados del modelo se desarrolla un analisis detallado de la influencia de estos parametros sobre la distribucion de irreversibilidades internas a lo largo del colector. Adicionalmente se estudia la influencia de estos parametros sobre los numeros de generacion de entropia por friccion viscosa, por transferencia de calor y total. Se encuentra que existen combinaciones de los parametros antes mencionados, para los cuales, la operacion del colector es termodinamicamente optima para numeros de flujo de masa elevados.

The influence of liquid/vapor phase change onto the Nusselt number

Science.gov (United States)

Popescu, Elena-Roxana; Colin, Catherine; Tanguy, Sebastien

2017-11-01

In spite of its significant interest in various fields, there is currently a very few information on how an external flow will modify the evaporation or the condensation of a liquid surface. Although most applications involve turbulent flows, the simpler configuration where a laminar superheated or subcooled vapor flow is shearing a saturated liquid interface has still never been solved. Based on a numerical approach, we propose to characterize the interaction between a laminar boundary layer of a superheated or subcooled vapor flow and a static liquid pool at saturation temperature. By performing a full set of simulations sweeping the parameters space, correlations are proposed for the first time on the Nusselt number depending on the dimensionless numbers that characterize both vaporization and condensation. As attended, the Nusselt number decreases or increases in the configurations involving respectively vaporization or condensation. More unexpected is the behaviour of the friction of the vapor flow on the liquid pool, for which we report that it is weakly affected by the phase change, despite the important variation of the local flow structure due to evaporation or condensation.

Statistical modeling of geopressured geothermal reservoirs

Science.gov (United States)

Ansari, Esmail; Hughes, Richard; White, Christopher D.

2017-06-01

Identifying attractive candidate reservoirs for producing geothermal energy requires predictive models. In this work, inspectional analysis and statistical modeling are used to create simple predictive models for a line drive design. Inspectional analysis on the partial differential equations governing this design yields a minimum number of fifteen dimensionless groups required to describe the physics of the system. These dimensionless groups are explained and confirmed using models with similar dimensionless groups but different dimensional parameters. This study models dimensionless production temperature and thermal recovery factor as the responses of a numerical model. These responses are obtained by a Box-Behnken experimental design. An uncertainty plot is used to segment the dimensionless time and develop a model for each segment. The important dimensionless numbers for each segment of the dimensionless time are identified using the Boosting method. These selected numbers are used in the regression models. The developed models are reduced to have a minimum number of predictors and interactions. The reduced final models are then presented and assessed using testing runs. Finally, applications of these models are offered. The presented workflow is generic and can be used to translate the output of a numerical simulator into simple predictive models in other research areas involving numerical simulation.

Baryon-plus-lepton number violation at high temperatures for arbitrary Higgs mass

International Nuclear Information System (INIS)

Li, Xu.

1992-01-01

In this thesis, baryon-plus lepton (B + L) number violation in the electroweak theory of the Weinberg-Salam model is systematically studied. B + L number non-conservation in the electroweak theory is believed to be a consequence of the axial U(1) anomaly. It is argued that sphaleron, not instanton dominates the topological vacuum-to-vacuum transitions for B + L number change at high temperatures. The rate of change is reduced to a dimensionless prefactor κ which is related to the determinants of small fluctuations around the sphaleron configuration. And κ is exactly computed at high temperatures exploiting symmetries of sphaleron under spatial rotations combined with isospin and custodial SU(2) transformations. For the ratio λ/g 2 of scalar four point coupling λ to gauge coupling g 2 near unity, it is found that κ is 0.03 and the rate of B + L number change at temperatures of order 1 Tev is about 8 to 9 orders of magnitude faster than the expansion rate of the big band theory. For λ/g 2 very small tending to the Coleman-Weinberg limit, it is found that the determinant strongly suppresses the rate of baryon number changing processes

A dimensionless ordered pull-through model of the mammalian lens epithelium evidences scaling across species and explains the age-dependent changes in cell density in the human lens

Science.gov (United States)

Wu, Jun Jie; Wu, Weiju; Tholozan, Frederique M.; Saunter, Christopher D.; Girkin, John M.; Quinlan, Roy A.

2015-01-01

We present a mathematical (ordered pull-through; OPT) model of the cell-density profile for the mammalian lens epithelium together with new experimental data. The model is based upon dimensionless parameters, an important criterion for inter-species comparisons where lens sizes can vary greatly (e.g. bovine (approx. 18 mm); mouse (approx. 2 mm)) and confirms that mammalian lenses scale with size. The validated model includes two parameters: β/α, which is the ratio of the proliferation rate in the peripheral and in the central region of the lens; and γGZ, a dimensionless pull-through parameter that accounts for the cell transition and exit from the epithelium into the lens body. Best-fit values were determined for mouse, rat, rabbit, bovine and human lens epithelia. The OPT model accounts for the peak in cell density at the periphery of the lens epithelium, a region where cell proliferation is concentrated and reaches a maximum coincident with the germinative zone. The β/α ratio correlates with the measured FGF-2 gradient, a morphogen critical to lens cell survival, proliferation and differentiation. As proliferation declines with age, the OPT model predicted age-dependent changes in cell-density profiles, which we observed in mouse and human lenses. PMID:26236824

Scaling Analysis of the Single-Phase Natural Circulation: the Hydraulic Similarity

International Nuclear Information System (INIS)

Yu, Xin-Guo; Choi, Ki-Yong

2015-01-01

These passive safety systems all rely on the natural circulation to cool down the reactor cores during an accident. Thus, a robust and accurate scaling methodology must be developed and employed to both assist in the design of a scaled-down test facility and guide the tests in order to mimic the natural circulation flow of its prototype. The natural circulation system generally consists of a heat source, the connecting pipes and several heat sinks. Although many applauding scaling methodologies have been proposed during last several decades, few works have been dedicated to systematically analyze and exactly preserve the hydraulic similarity. In the present study, the hydraulic similarity analyses are performed at both system and local level. By this mean, the scaling criteria for the exact hydraulic similarity in a full-pressure model have been sought. In other words, not only the system-level but also the local-level hydraulic similarities are pursued. As the hydraulic characteristics of a fluid system is governed by the momentum equation, the scaling analysis starts with it. A dimensionless integral loop momentum equation is derived to obtain the dimensionless numbers. In the dimensionless momentum equation, two dimensionless numbers, the dimensionless flow resistance number and the dimensionless gravitational force number, are identified along with a unique hydraulic time scale, characterizing the system hydraulic response. A full-height full-pressure model is also made to see which model among the full-height model and reduced-height model can preserve the hydraulic behavior of the prototype. From the dimensionless integral momentum equation, a unique hydraulic time scale, which characterizes the hydraulic response of a single-phase natural circulation system, is identified along with two dimensionless parameters: the dimensionless flow resistance number and the dimensionless gravitational force number. By satisfying the equality of both dimensionless numbers

Scaling Analysis of the Single-Phase Natural Circulation: the Hydraulic Similarity

Energy Technology Data Exchange (ETDEWEB)

Yu, Xin-Guo; Choi, Ki-Yong [KAERI, Daejeon (Korea, Republic of)

2015-05-15

These passive safety systems all rely on the natural circulation to cool down the reactor cores during an accident. Thus, a robust and accurate scaling methodology must be developed and employed to both assist in the design of a scaled-down test facility and guide the tests in order to mimic the natural circulation flow of its prototype. The natural circulation system generally consists of a heat source, the connecting pipes and several heat sinks. Although many applauding scaling methodologies have been proposed during last several decades, few works have been dedicated to systematically analyze and exactly preserve the hydraulic similarity. In the present study, the hydraulic similarity analyses are performed at both system and local level. By this mean, the scaling criteria for the exact hydraulic similarity in a full-pressure model have been sought. In other words, not only the system-level but also the local-level hydraulic similarities are pursued. As the hydraulic characteristics of a fluid system is governed by the momentum equation, the scaling analysis starts with it. A dimensionless integral loop momentum equation is derived to obtain the dimensionless numbers. In the dimensionless momentum equation, two dimensionless numbers, the dimensionless flow resistance number and the dimensionless gravitational force number, are identified along with a unique hydraulic time scale, characterizing the system hydraulic response. A full-height full-pressure model is also made to see which model among the full-height model and reduced-height model can preserve the hydraulic behavior of the prototype. From the dimensionless integral momentum equation, a unique hydraulic time scale, which characterizes the hydraulic response of a single-phase natural circulation system, is identified along with two dimensionless parameters: the dimensionless flow resistance number and the dimensionless gravitational force number. By satisfying the equality of both dimensionless numbers

On two distinct Reynolds number regimes of a turbulent square jet

Directory of Open Access Journals (Sweden)

Minyi Xu

2015-05-01

Full Text Available The effects of Reynolds number on both large-scale and small-scale turbulence properties are investigated in a square jet issuing from a square pipe. The detailed velocity fields were measured at five different exit Reynolds numbers of 8×103≤Re≤5×104. It is found that both large-scale properties (e.g., rates of mean velocity decay and spread and small-scale properties (e.g., the dimensionless dissipation rate constant A=εL/〈u2〉3/2 are dependent on Re for Re≤3×104 or Reλ≤190, but virtually become Re-independent with increasing Re or Reλ. In addition, for Reλ>190, the value of A=εL/〈u2〉3/2 in the present square jet converges to 0.5, which is consistent with the observation in direct numerical simulations of box turbulence, but lower than that in circular jet, plate wake flows, and grid turbulence. The discrepancies in critical Reynolds number and A=εL/〈u2〉3/2 among different turbulent flows most likely result from the flow type and initial conditions.

Deformation of ferrofluid marbles in the presence of a permanent magnet.

Science.gov (United States)

Nguyen, Nam-Trung

2013-11-12

This paper investigates the deformation of ferrofluid marbles in the presence of a permanent magnet. Ferrofluid marbles are formed using a water-based ferrofluid and 1 μm hydrophobic polytetrafluoride particles. A marble placed on a Teflon coated glass plate deforms under gravity. In the presence of a permanent magnet, the marble is further deformed with a larger contact area. The geometric parameters are normalized by the radius of an undistorted spherical marble. The paper first discusses a scaling relationship between the dimensionless radius of the contact area as well as the dimensionless height and the magnetic Bond number. The dimensionless contact radius is proportional to the fourth root of the magnetic bond number. The dimensionless height scales with the inverse square root of the magnetic Bond number. In the case of a moving marble dragged by a permanent magnet, the deformation is evaluated as the difference between advancing and receding curvatures of the top view. The dimensionless height and the contact diameter of the marble do not significantly depend on the speed or the capillary number. The scaling analysis and experimental data show that the deformation is proportional to the capillary number.

Useful scaling parameters for the pulse tube

International Nuclear Information System (INIS)

Lee, J.M.; Kittel, P.; Timmerhaus, K.D.

1996-01-01

A set of dimensionless scaling parameters for use in correlating performance data for Pulse Tube Refrigerators is presented. The dimensionless groups result after scaling the mass and energy conservation equations, and the equation of motion for an axisymmetric, two-dimensional ideal gas system. Allowed are viscous effects and conduction heat transfer between the gas and the tube wall. The scaling procedure results in reducing the original 23 dimensional variables to a set of 11 dimensionless scaling groups. Dimensional analysis is used to verify that the 11 dimensionless groups obtained is the minimum number needed to describe the system. The authors also examine 6 limiting cases which progressively reduce the number of dimensionless groups from 11 to 3. The physical interpretation of the parameters are described, and their usefulness is outlined for understanding how heat transfer and mass streaming affect ideal enthalpy flow

Prediction of local loss coefficient for turbulent flow in axisymmetric sudden expansions with a chamfer: Effect of Reynolds number

International Nuclear Information System (INIS)

Bae, Youngmin; Kim, Young In

2014-01-01

Highlights: • Turbulent flow in axisymmetric sudden expansion with a chamfer is studied numerically. • Reynolds number dependency of the local loss coefficient is investigated. • Extended correlation is proposed for estimation of the local loss coefficient. - Abstract: This paper reports the pressure losses in turbulent flows through axisymmetric sudden expansions having a slight chamfer on the edge. A parametric study is performed for dimensionless chamfer lengths of 0–0.5, expansion ratios of 2–6, and chamfer angles of 0–45° in a Reynolds number range of 1 × 10 5 –8 × 10 5 . The chamfer effect on the expansion losses and its dependence on the Reynolds number are analyzed in detail along with a discussion of the relevant flow features. On the basis of numerical results, an existing correlation of the local loss coefficient is also extended to take into account the effect of the Reynolds number additionally

Mixed Convection Flow of Magnetic Viscoelastic Polymer from a Nonisothermal Wedge with Biot Number Effects

Directory of Open Access Journals (Sweden)

S. Abdul Gaffar

2015-01-01

Full Text Available Magnetic polymers are finding increasing applications in diverse fields of chemical and mechanical engineering. In this paper, we investigate the nonlinear steady boundary layer flow and heat transfer of such fluids from a nonisothermal wedge. The incompressible Eyring-Powell non-Newtonian fluid model is employed and a magnetohydrodynamic body force is included in the simulation. The transformed conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite difference Keller Box technique. The numerical code is validated with previous studies. The influence of a number of emerging nondimensional parameters, namely, the Eyring-Powell rheological fluid parameter (ε, local non-Newtonian parameter based on length scale (δ, Prandtl number (Pr, Biot number (γ, pressure gradient parameter (m, magnetic parameter (M, mixed convection parameter (λ, and dimensionless tangential coordinate (ξ, on velocity and temperature evolution in the boundary layer regime is examined in detail. Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated.

Relaxation-type nonlocal inertial-number rheology for dry granular flows

Science.gov (United States)

Lee, Keng-lin; Yang, Fu-ling

2017-12-01

We propose a constitutive model to describe the nonlocality, hysteresis, and several flow features of dry granular materials. Taking the well-known inertial number I as a measure of sheared-induced local fluidization, we derive a relaxation model for I according to the evolution of microstructure during avalanche and dissipation processes. The model yields a nonmonotonic flow law for a homogeneous flow, accounting for hysteretic solid-fluid transition and intermittency in quasistatic flows. For an inhomogeneous flow, the model predicts a generalized Bagnold shear stress revealing the interplay of two microscopic nonlocal mechanisms: collisions among correlated structures and the diffusion of fluidization within the structures. In describing a uniform flow down an incline, the model reproduces the hysteretic starting and stopping heights and the Pouliquen flow rule for mean velocity. Moreover, a dimensionless parameter reflecting the nonlocal effect on the flow is discovered, which controls the transition between Bagnold and creeping flow dynamics.

The effect of heat generation in inclined slats on the natural convective heat transfer from an isothermal heated vertical plate

International Nuclear Information System (INIS)

Oosthuizen, P.H.; Sun, L.; Naylor, D.

2003-01-01

Natural convective heat transfer from a wide heated vertical isothermal plate with adiabatic surfaces above and below the heated surface has been considered. There are a series of equally spaced vertical thin, flat surfaces (termed 'slats') near the heated surface, these surfaces being, in general, inclined to the heated surface. There is, in general, a uniform heat generation in the slats. The slats are pivoted about their centre-point and thus as their angle is changed, the distance of the tip of the slat from the plate changes. The situation considered is an approximate model of a window with a vertical blind, the particular case where the window is hotter than the room air being considered. The heat generation in the slats in this situation is the result of solar radiation passing through the window and falling on and being absorbed by the slats of the blind. The flow has been assumed to be laminar and steady. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces. The governing equations have been written in dimensionless form and the resulting dimensionless equations have been solved using a commercial finite-element package. The solution has the following parameters: (1) the Rayleigh number (2) the Prandtl number (3) the dimensionless heat generation rate in the slats per unit frontal area (4) the dimensionless distance of the slat center point (the pivot point) from the surface (5) the dimensionless slat size (6) the dimensionless slat spacing (7) the angle of inclination of the slats. Because of the application that motivated the study, results have only been obtained for a Prandtl number of 0.7. The effect of the other dimensionless variables on the mean dimensionless heat transfer rate from the heated vertical surface has been examined. (author)

PHOTOSPHERE EMISSION FROM A HYBRID RELATIVISTIC OUTFLOW WITH ARBITRARY DIMENSIONLESS ENTROPY AND MAGNETIZATION IN GRBs

Energy Technology Data Exchange (ETDEWEB)

Gao, He [Current address: Department of Astronomy and Astrophysics, Department of Physics, Center for Particle Astrophysics, Pennsylvania State University, University Park, PA 16802 (United States); Zhang, Bing, E-mail: gaohe@physics.unlv.edu, E-mail: zhang@physics.unlv.edu, E-mail: hug18@psu.edu [Department of Physics and Astronomy, University of Nevada, Las Vegas, NV 89154 (United States)

2015-03-10

In view of the recent Fermi observations of gamma-ray burst (GRB) prompt emission spectra, we develop a theory of photosphere emission of a hybrid relativistic outflow with a hot fireball component (defined by dimensionless entropy η) and a cold Poynting-flux component (defined by magnetization σ{sub 0} at the central engine). We consider the scenarios both without and with sub-photospheric magnetic dissipations. Based on a simplified toy model of jet dynamics, we develop two approaches: a 'bottom-up' approach to predict the temperature (for a non-dissipative photosphere) and luminosity of the photosphere emission and its relative brightness for a given pair of (η, σ{sub 0}); and a 'top-down' approach to diagnose central engine parameters (η and σ{sub 0}) based on the observed quasi-thermal photosphere emission properties. We show that a variety of observed GRB prompt emission spectra with different degrees of photosphere thermal emission can be reproduced by varying η and σ{sub 0} within the non-dissipative photosphere scenario. In order to reproduce the observed spectra, the outflows of most GRBs need to have a significant σ, both at the central engine and at the photosphere. The σ value at 10{sup 15} cm from the central engine (a possible non-thermal emission site) is usually also greater than unity, so that internal-collision-induced magnetic reconnection and turbulence (ICMART) may be the mechanism to power the non-thermal emission. We apply our top-down approach to GRB 110721A and find that the temporal evolution behavior of its blackbody component can be well interpreted with a time-varying (η, σ{sub 0}) at the central engine, instead of invoking a varying engine base size r {sub 0} as proposed by previous authors.

DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers

International Nuclear Information System (INIS)

Schwertfirm, Florian; Manhart, Michael

2007-01-01

We perform DNS of passive scalar transport in low Reynolds number turbulent channel flow at Schmidt numbers up to Sc = 49. The high resolutions required to resolve the scalar concentration fields at such Schmidt numbers are achieved by a hierarchical algorithm in which only the scalar fields are solved on the grid dictated by the Batchelor scale. The velocity fields are solved on coarser grids and prolonged by a conservative interpolation to the fine-grid. The trends observed so far at lower Schmidt numbers Sc ≤ 10 are confirmed, i.e. the mean scalar gradient steepens at the wall with increasing Schmidt number, the peaks of turbulent quantities increase and move towards the wall. The instantaneous scalar fields show a dramatic change. Observable structures get longer and thinner which is connected with the occurrence of steeper gradients, but the wall concentrations penetrate less deeply into the plateau in the core of the channel. Our data shows that the thickness of the conductive sublayer, as defined by the intersection point of the linear with the logarithmic asymptote scales with Sc -0.29 . With this information it is possible to derive an expression for the dimensionless transfer coefficient K + which is only dependent on Sc and Re τ . This expression is in full accordance to previous results which demonstrates that the thickness of the conductive sublayer is the dominating quantity for the mean scalar profile

DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers

Energy Technology Data Exchange (ETDEWEB)

Schwertfirm, Florian [Fachgebiet Hydromechanik, Technische Universitaet Muenchen, Arcisstr. 21, 80337 Muenchen (Germany); Manhart, Michael [Fachgebiet Hydromechanik, Technische Universitaet Muenchen, Arcisstr. 21, 80337 Muenchen (Germany)], E-mail: m.manhart@bv.tum.de

2007-12-15

We perform DNS of passive scalar transport in low Reynolds number turbulent channel flow at Schmidt numbers up to Sc = 49. The high resolutions required to resolve the scalar concentration fields at such Schmidt numbers are achieved by a hierarchical algorithm in which only the scalar fields are solved on the grid dictated by the Batchelor scale. The velocity fields are solved on coarser grids and prolonged by a conservative interpolation to the fine-grid. The trends observed so far at lower Schmidt numbers Sc {<=} 10 are confirmed, i.e. the mean scalar gradient steepens at the wall with increasing Schmidt number, the peaks of turbulent quantities increase and move towards the wall. The instantaneous scalar fields show a dramatic change. Observable structures get longer and thinner which is connected with the occurrence of steeper gradients, but the wall concentrations penetrate less deeply into the plateau in the core of the channel. Our data shows that the thickness of the conductive sublayer, as defined by the intersection point of the linear with the logarithmic asymptote scales with Sc{sup -0.29}. With this information it is possible to derive an expression for the dimensionless transfer coefficient K{sup +} which is only dependent on Sc and Re{sub {tau}}. This expression is in full accordance to previous results which demonstrates that the thickness of the conductive sublayer is the dominating quantity for the mean scalar profile.

Fluid flow in gas condensate reservoirs. The interplay of forces and their relative strengths

Energy Technology Data Exchange (ETDEWEB)

Ursin, Jann-Rune [Stavanger University College, Department of Petroleum Engineering, PO Box 8002, Stavanger, 4068 (Norway)

2004-02-01

Natural production from gas condensate reservoirs is characterized by gas condensation and liquid dropout in the reservoir, first in the near wellbore volume, then as a cylindrical shaped region, dynamically developing into the reservoir volume. The effects of liquid condensation are reduced productivity and loss of production. Successful forecast of well productivity and reservoir production depends on detailed understanding of the effect of various forces acting on fluid flow in time and space. The production form gas condensate reservoirs is thus indirectly related to the interplay of fundamental forces, such as the viscosity, the capillary, the gravitational and the inertial force and their relative strengths, demonstrated by various dimensionless numbers. Dimensionless numbers are defined and calculated for all pressure and space coordinates in a test reservoir. Various regions are identified where certain forces are more important than others. Based on reservoir pressure development, liquid condensation and the numerical representation of dimensionless numbers, a conceptual understanding of a varying reservoir permeability has been reached.The material balance, the reservoir fluid flow and the wellbore flow calculations are performed on a cylindrical reservoir model. The ratios between fundamental forces are calculated and dimensionless numbers defined. The interplay of forces, demonstrated by these numbers, are calculated as function of radial dimension and reservoir pressure.

A dimensionless dynamic contrast enhanced MRI parameter for intra-prostatic tumour target volume delineation: initial comparison with histology

Science.gov (United States)

Hrinivich, W. Thomas; Gibson, Eli; Gaed, Mena; Gomez, Jose A.; Moussa, Madeleine; McKenzie, Charles A.; Bauman, Glenn S.; Ward, Aaron D.; Fenster, Aaron; Wong, Eugene

2014-03-01

Purpose: T2 weighted and diffusion weighted magnetic resonance imaging (MRI) show promise in isolating prostate tumours. Dynamic contrast enhanced (DCE)-MRI has also been employed as a component in multi-parametric tumour detection schemes. Model-based parameters such as Ktrans are conventionally used to characterize DCE images and require arterial contrast agent (CR) concentration. A robust parameter map that does not depend on arterial input may be more useful for target volume delineation. We present a dimensionless parameter (Wio) that characterizes CR wash-in and washout rates without requiring arterial CR concentration. Wio is compared to Ktrans in terms of ability to discriminate cancer in the prostate, as demonstrated via comparison with histology. Methods: Three subjects underwent DCE-MRI using gadolinium contrast and 7 s imaging temporal resolution. A pathologist identified cancer on whole-mount histology specimens, and slides were deformably registered to MR images. The ability of Wio maps to discriminate cancer was determined through receiver operating characteristic curve (ROC) analysis. Results: There is a trend that Wio shows greater area under the ROC curve (AUC) than Ktrans with median AUC values of 0.74 and 0.69 respectively, but the difference was not statistically significant based on a Wilcoxon signed-rank test (p = 0.13). Conclusions: Preliminary results indicate that Wio shows potential as a tool for Ktrans QA, showing similar ability to discriminate cancer in the prostate as Ktrans without requiring arterial CR concentration.

The effect of inclined vertical slats on natural convective heat transfer from an isothermal heated vertical plate

International Nuclear Information System (INIS)

Oosthuizen, P.H.; Sun, L.; Naylor, D.

2002-01-01

Natural convective heat transfer from a wide heated vertical isothermal plate with adiabatic surfaces above and below the heated surface has been considered. There are a series of equally spaced vertical thin, flat adiabatic surfaces (termed 'slats') near the heated surface, these surfaces being, in general, inclined to the heated surface. The slats are pivoted about their center-point and thus as their angle is changed, the distance of the tip of the slat from the plate changes. The situation considered is an approximate model of a window with a vertical blind, the particular case where the window is hotter than the room air, i.e. where air-conditioning is being used, being considered. The flow has been assumed to be laminar and steady. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being treated by means of the Biuniqueness type approximation. Although the flow is in general three-dimensional, the flow over each slat is assumed to be the same and attention can therefore be restricted to flow over a single slat by using repeating boundary conditions. The governing equations have been written in dimensionless form and the resulting dimensionless equations have been solved using a commercial finite-element package. The solution has the following parameters: (1) the Rayleigh number (2) the Prandtl number (3) the dimensionless distance of the slat center point (the pivot point) from the surface (4) the dimensionless slat size (5) the dimensionless slat spacing (6) the angle of inclination of the slats. Because of the application that motivated the study, results have only been obtained for a Prandtl number of 0.7. The effect of the other dimensionless variables on the mean dimensionless heat transfer rate from the heated surface has been examined. (author)

A stydy on the heat transfer characteristics in the composite heat pipe as modeling turbine rotor

International Nuclear Information System (INIS)

Kwon, Sun Sok; Jang, Yeong Suc; Yoo, Byung Wook

1993-01-01

The purpose of this research is to study the characteristics of heat transfer in composite rotary heat pipe as modeled turbine rotating by a finite element analysis and experiment. Nu number, Re number, Pr number and dimensionless condensate layer thickness by thermal input and revolutions per minute were given as analysis factors. The comparison between calculated and experimental data showed similar tendency. Therefore the analysis method may be useful to predict the performance of composite heat pipe. The resistance on heat pipe showed the best effect of heat transfer by film condensation, by decreasing film condensation, the heat transfer rate from condenser was increased rapidly. The dimensionless condensate layer thickness according to Re number at given Pr number showed constant values, the dimensionless condensate layer thickness is proportionate to the square root of inverse of revolution number per minute. In this study Nu = A(δ(ω/ν) -1/2 Re B ) is used to the convection heat transfer coefficient and A = 0.963, B = 0.5025 were obtained as analysis predicts. (Author)

Effect of Magnetic Field on Entropy Generation Due to Laminar Forced Convection Past a Horizontal Flat Plate

Directory of Open Access Journals (Sweden)

Moh'd A. Al-Nimr

2004-06-01

Full Text Available Magnetic field effect on local entropy generation due to steady two-dimensional laminar forced convection flow past a horizontal plate was numerically investigated. This study was focused on the entropy generation characteristics and its dependency on various dimensionless parameters. The effect of various dimensionless parameters, such as Hartmann number (Ha, Eckert number (Ec, Prandtl number (Pr, Joule heating parameter (R and the free stream temperature parameter (θ∞ on the entropy generation characteristics is analyzed. The dimensionless governing equations in Cartesian coordinate were solved by an implicit finite difference technique. The solutions were carried out for Ha2=0.5-3, Ec=0.01-0.05, Pr=1-5 and θ∞=1.1-2.5. It was found that, the entropy generation increased with increasing Ha, Ec and R. While, increasing the free stream temperature parameter, and Prandtl number tend to decrease the local entropy generation.

Theoretical Analysis of Effects of Wall Suction on Entropy Generation Rate in Laminar Condensate Layer on Horizontal Tube

Directory of Open Access Journals (Sweden)

Tong-Bou Chang

2014-01-01

Full Text Available The effects of wall suction on the entropy generation rate in a two-dimensional steady film condensation flow on a horizontal tube are investigated theoretically. In analyzing the liquid flow, the effects of both the gravitational force and the viscous force are taken into account. In addition, a film thickness reduction ratio, Sf, is introduced to evaluate the effect of wall suction on the thickness of the condensate layer. The analytical results show that, the entropy generation rate depends on the Jakob number Ja, the Rayleigh number Ra, the Brinkman number Br, the dimensionless temperature difference ψ, and the wall suction parameter Sw. In addition, it is shown that in the absence of wall suction, a closed-form correlation for the Nusselt number can be derived. Finally, it is shown that the dimensionless entropy generation due to heat transfer, NT, increases with an increasing suction parameter Sw, whereas the dimensionless entropy generation due to liquid film flow friction, NF, decreases.

Effects of Froude number and geometry on water entry of a 2-D ellipse

Science.gov (United States)

Zhang, Xu; Liu, Pei-qing; Qu, Qiu-lin; Wang, Rui; Agarwal, Ramesh K.

2018-05-01

By using the finite volume method with volume of fluid model and global dynamic mesh technique, the effects of Froude number and geometry on the water entry process of a 2-D ellipse are investigated numerically. For the time history of the vertical force, the computational fluid dynamics (CFD) results match the experimental data much better than the classical potential-flow theories due to the consideration of the viscosity, turbulence, surface tension, gravity, and compressibility. The results show that the position of peak pressure on ellipse shifts from the spray root to the bottom of ellipse at a critical time. The critical time changes with the geometry and Froude number. By studying the vertical force, the ellipse water entry process can be divided into the initial and late stages based on the critical dimensionless time of about 0.1. The geometry of the ellipse plays a dominant role in the initial stage, while the Froude number is more important in the late stage of entry. The classical Wagner theory is extended to the ellipse water entry, and the predicted maximum value of vertical force coefficient in the initial stage is 4πa/b that matches the CFD results very well, where a and b are the horizontal axis and vertical axis of the ellipse parallel and perpendicular to the initial calm water surface, respectively.

Unsteady MHD blood flow through porous medium in a parallel plate channel

Science.gov (United States)

Latha, R.; Rushi Kumar, B.

2017-11-01

In this study, we have analyzed heat and mass transfer effects on unsteady blood flow through parallel plate channel in a saturated porous medium in the presence of a transverse magnetic field with thermal radiation. The governing higher order nonlinear PDE’S are converted to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using boundary conditions by choosing the axial flow transport and the fields of concentration and temperature apart from the normal velocity as a function of y and t. The effects of different pertinent parameters appeared in this model viz thermal radiation, Prandtl number, Heat source parameter, Hartmann number, Permeability parameter, Decay parameter on axial flow transport and the normal velocity are analyzed in detail.

OFF-DESIGN OPERATION OF IMPELLER OF THE CENTRIFUGAL COMPRESSOR

Directory of Open Access Journals (Sweden)

Saim KOÇAK

2004-02-01

Full Text Available Inducer and discharge dimensions of impellers of centrifugal compressor are determined as a preliminary design. Blockage factor and inducer dimensionless mass flow are exercised in relation with the relative Mach number. The equation which will be based o off-design calculation, related with the discharge relative Mach number are iterated until it will equal to inducer dimensionless mass flow rate. Then discharge relative Mach number for off-design works is obtained. The results calculated in accordance with pressure, temperature and density are seen to be similar with the theoretical parameters.

Analysis of effect of temperature gradients on surface-tension phenomena in gas-tungsten-arc welds

International Nuclear Information System (INIS)

Lee, H.A.; Chien, P.S.J.

1982-10-01

Fluid motion directed by surface tension is considered as a contributor to heat penetration in a weld pool. The potential phenomena at the gas-liquid interface were analyzed, and the dependence of surface motion on temperature in the gas-tungsten-arc (GTA) welding process was examined. An existing heat-transfer model was used and was able to predict weld size to +- 50% of the actual value. A momentum-transfer equation was derived by considering the contribution of Lorentz force. The momentum boundary condition was developed and was able to predict the Marangoni effect. The magnitude of surface-tension-driven force is comparable to the gravitational force on one gram. An empirical approach was proposed to couple heat-transfer and momentum-transfer phenomena. A dimensional analysis identified the pertinent dimensionless groups as Reynolds, Weber, Froude, Peclet, and Power numbers and a dimensionless velocity. A simplified form of the correction was developed by combining dimensionless groups to yield a correlation with the Bond, Prandtl, and modified power numbers. Future experimental work was proposed to test the functionality of the dimensionless groups

Numerical and dimensional investigation of two-phase countercurrent imbibition in porous media

KAUST Repository

El-Amin, Mohamed

2013-04-01

In this paper, we introduce a numerical solution of the problem of two-phase immiscible flow in porous media. In the first part of this work, we present the general conservation laws for multiphase flows in porous media as outlined in the literature for the sake of completion where we emphasize the difficulties associated with these equations in their primitive form and the fact that they are, generally, unclosed. The second part concerns the 1D computation for dimensional and non-dimensional cases and a theoretical analysis of the problem under consideration. A time-scale based on the characteristic velocity is used to transform the macroscopic governing equations into a non-dimensional form. The resulting dimensionless governing equations involved some important dimensionless physical parameters such as Bond number Bo, capillary number Ca and Darcy number Da. Numerical experiments on the Bond number effect is performed for two cases, gravity opposing and assisting. The theoretical analysis illustrates that common formulations of the time-scale forces the coefficient Da12Ca to be equal to one, while formulation of dimensionless time based on a characteristic velocity allows the capillary and Darcy numbers to appear in the dimensionless governing equation which leads to a wide range of scales and physical properties of fluids and rocks. The results indicate that the buoyancy effects due to gravity force take place depending on the location of the open boundary. © 2012 Elsevier B.V. All rights reserved.

Soret and Dufour effects on convective heat and mass transfer in stagnation-point flow towards a shrinking surface

International Nuclear Information System (INIS)

Bhattacharyya, Krishnendu; Layek, G C; Seth, G S

2014-01-01

A mathematical model is presented to study the Soret and Dufour effects on the convective heat and mass transfer in stagnation-point flow of viscous incompressible fluid towards a shrinking surface. Suitable similarity transformations are used to convert the governing partial differential equations into self-similarity ordinary differential equations that are then numerically solved by shooting method. Dual solutions for temperature and concentration are obtained in the presence of Soret and Dufour effects. Graphical representations of the heat and mass transfer coefficients, the dimensionless thermal and solute profiles for various values of Prandtl number, Lewis number, Soret number and Dufour number are demonstrated. With Soret number the mass transfer coefficient which is related to mass transfer rate increases for both solutions and the heat transfer coefficient (related to heat transfer rate) for both solutions becomes larger with Dufour number. The Prandtl number causes reduction in heat and the mass transfer coefficients and similarly with the Lewis number mass transfer coefficient decreases. Also, double crossing over is found in dual dimensionless temperature profiles for increasing Soret number and in dual dimensionless concentration profiles for the increase in Dufour number. Due to the larger values of Dufour number the thermal boundary layer increases and for Prandtl number increment it decreases; whereas, the solute boundary layer thickness reduces with increasing values of Prandtl number and Lewis number. (paper)

Analysis of activation energy in Couette-Poiseuille flow of nanofluid in the presence of chemical reaction and convective boundary conditions

Science.gov (United States)

Zeeshan, A.; Shehzad, N.; Ellahi, R.

2018-03-01

The motivation of the current article is to explore the energy activation in MHD radiative Couette-Poiseuille flow nanofluid in horizontal channel with convective boundary conditions. The mathematical model of Buongiorno [1] effectively describes the current flow analysis. Additionally, the impact of chemical reaction is also taken in account. The governing flow equations are simplified with the help of boundary layer approximations. Non-linear coupled equations for momentum, energy and mass transfer are tackled with analytical (HAM) technique. The influence of dimensionless convergence parameter like Brownian motion parameter, radiation parameter, buoyancy ratio parameter, dimensionless activation energy, thermophoresis parameter, temperature difference parameter, dimensionless reaction rate, Schmidt number, Brinkman number, Biot number and convection diffusion parameter on velocity, temperature and concentration profiles are discussed graphically and in tabular form. From the results, it is elaborate that the nanoparticle concentration is directly proportional to the chemical reaction with activation energy and the performance of Brownian motion on nanoparticle concentration gives reverse pattern to that of thermophoresis parameter.

Scale-up of bioreactors: The concept of bioreactor number and its relation to the physiology of industrial microorganisms at different scales

Energy Technology Data Exchange (ETDEWEB)

De Ford, D

1988-01-01

The objective of this research is to provide a novel approach to the problem of scale-up of fermentations. The work subscribes the idea that two regions appear in bioreactors as the volume increases. The first is where high oxygen transfer occurs and the second is where low oxygen transfer occurs. It is assumed that organisms grown in a stirred tank fermenter travel in a cyclical manner through these two regions. A dimensionless factor is developed, the bioreactor number. Using this number the performance of any stirred tank fermenter can be described as a function of its geometry, operating conditions and physical properties of media. A mathematical model for the prediction of the physiological response of aerobic micro-organisms (specific growth rate, final cell concentration and product synthesis) as a function of the bioreactor number is also developed. It was adjusted by using the results of fermentations performed in a specially designed experimental rig allowing the simulation of fermenters with various bioreactor numbers. If the bioreactor and physiological models are linked it is possible to predict how micro-organisms respond when geometry, operating conditions or media properties are changed in a bioreactor. This approach is a tool for decision making in the design and operation of fermenters.

The large numbers hypothesis and the Einstein theory of gravitation

International Nuclear Information System (INIS)

Dirac, P.A.M.

1979-01-01

A study of the relations between large dimensionless numbers leads to the belief that G, expressed in atomic units, varies with the epoch while the Einstein theory requires G to be constant. These two requirements can be reconciled by supposing that the Einstein theory applies with a metric that differs from the atomic metric. The theory can be developed with conservation of mass by supposing that the continual increase in the mass of the observable universe arises from a continual slowing down of the velocity of recession of the galaxies. This leads to a model of the Universe that was first proposed by Einstein and de Sitter (the E.S. model). The observations of the microwave radiation fit in with this model. The static Schwarzchild metric has to be modified to fit in with the E.S. model for large r. The modification is worked out, and also the motion of planets with the new metric. It is found that there is a difference between ephemeris time and atomic time, and also that there should be an inward spiralling of the planets, referred to atomic units, superposed on the motion given by ordinary gravitational theory. These are effects that can be checked by observation, but there is no conclusive evidence up to the present. (author)

Numerical simulation of flow past twin near-wall circular cylinders in tandem arrangement at low Reynolds number

Directory of Open Access Journals (Sweden)

Guo-qiang Tang

2015-10-01

Full Text Available Fluid flow past twin circular cylinders in a tandem arrangement placed near a plane wall was investigated by means of numerical simulations. The two-dimensional Navier-Stokes equations were solved with a three-step finite element method at a relatively low Reynolds number of Re = 200 for various dimensionless ratios of and , where D is the cylinder diameter, L is the center-to-center distance between the two cylinders, and G is the gap between the lowest surface of the twin cylinders and the plane wall. The influences of and on the hydrodynamic force coefficients, Strouhal numbers, and vortex shedding modes were examined. Three different vortex shedding modes of the near wake were identified according to the numerical results. It was found that the hydrodynamic force coefficients and vortex shedding modes are quite different with respect to various combinations of and . For very small values of , the vortex shedding is completely suppressed, resulting in the root mean square (RMS values of drag and lift coefficients of both cylinders and the Strouhal number for the downstream cylinder being almost zero. The mean drag coefficient of the upstream cylinder is larger than that of the downstream cylinder for the same combination of and . It is also observed that change in the vortex shedding modes leads to a significant increase in the RMS values of drag and lift coefficients.

Universal dependences between turbulent and mean flow parameters instably and neutrally stratified Planetary Boundary Layers

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I. N. Esau

2006-01-01

Full Text Available We consider the resistance law for the planetary boundary layer (PBL from the point of view of the similarity theory. In other words, we select the set of the PBL governing parameters and search for an optimal way to express through these parameters the geostrophic drag coefficient Cg=u* /Ug and the cross isobaric angle α (where u* is the friction velocity and Ug is the geostrophic wind speed. By this example, we demonstrate how to determine the 'parameter space' in the most convenient way, so that make independent the dimensionless numbers representing co-ordinates in the parameter space, and to avoid (or at least minimise artificial self-correlations caused by the appearance of the same factors (such as u* in the examined dimensionless combinations (e.g. in Cg=u* /Ug and in dimensionless numbers composed of the governing parameters. We also discuss the 'completeness' of the parameter space from the point of view of large-eddy simulation (LES modeller creating a database for a specific physical problem. As recognised recently, very large scatter of data in prior empirical dependencies of Cg and α on the surface Rossby number Ro=Ug| fz0|-1 (where z0 is the roughness length and the stratification characterised by µ was to a large extent caused by incompactness of the set of the governing parameters. The most important parameter overlooked in the traditional approach is the typical value of the Brunt-Väisälä frequency N in the free atmosphere (immediately above the PBL, which involves, besides Ro and µ, one more dimensionless number: µN=N/ | f |. Accordingly, we consider Cg and α as dependent on the three (rather then two basic dimensionless numbers (including µN using LES database DATABASE64. By these means we determine the form of the dependencies under consideration in the part of the parameter space representing typical atmospheric PBLs, and provide analytical expressions for Cg and α.

CROSS-FLOW ULTRAFILTRATION OF SECONDARY EFFLUENTS. MEMBRANE FOULING ANALYSIS

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Luisa Vera

2014-12-01

Full Text Available The application of cross-flow ultrafiltration to regenerate secondary effluents is limited by membrane fouling. This work analyzes the influence of the main operational parameters (transmembrane pressure and cross-flow velocity about the selectivity and fouling observed in an ultrafiltration tubular ceramic membrane. The experimental results have shown a significant retention of the microcolloidal and soluble organic matter (52 – 54% in the membrane. The fouling analysis has defined the critical operational conditions where the fouling resistance is minimized. Such conditions can be described in terms of a dimensionless number known as shear stress number and its relationship with other dimensionless parameter, the fouling number.

AN EXPERIMENTAL STUDY FOR HEAT TRANSFER ENHANCEMENT BY LAMINAR FORCED CONVECTION FROM HORIZONTAL AND INCLINED TUBE HEATED WITH CONSTANT HEAT FLUX, USING TWO TYPES OF POROUS MEDIA

Directory of Open Access Journals (Sweden)

Thamir K. Jassem

2015-02-01

Full Text Available An experimental forced laminar study was presented in this research for an air flowing through a circular channel for different angles ( ,30o,45o,60o, the channel was heated at constant heat flux , the channel also was packed with steel and glass spheres respectively . The tests were done for three values of Peclets number (2111.71,3945.42,4575.47 with changing the heat flux for each case and five times for each number.The results showed that the dimensionless temperature distribution  will decrease with increasing the dimensionless channel length for all cases with changing Peclet number, heat flux and inclination angles, and its lowest value will be for glass spheres at highest flux, while at lower flux for , and the decreasing in dimensionless temperature was closed for both types of packed at other inclination angles.The study declared that the local Nusselt number decreases with increasing the dimensionless length of the channel for both packeds and for different applied heat flux, also through this study it was declared that the average Nusselt increases as Peclet number increases for both packed. Its value for the glass spheres is greater than the steel spheres with percentage (98.3% at small Peclet, and percentage (97.2% at large Peclet number for the horizontal tube, and (98.3% at small Peclet number and (97.8% at large Peclet number at  .Through this study its was found that average Nusselt number increases along the channel as the heat flux increases, because the bulk temperature will increase as the flow proceeds toward the end of the channel , so the heat transfer coefficient will increase.  It was declared from this study that in the case of the steel packed the heat transfer will occur mainly by conduction, while in the case of glass packed the heat transfer will occur mainly by laminar forced convection, where the lowest Nusselt number (Nu=3.8 was found when the pipe is horizontal and lowest heat flux and lowest Peclet number.  

Heat and Mass Transfer with Free Convection MHD Flow Past a Vertical Plate Embedded in a Porous Medium

Directory of Open Access Journals (Sweden)

Farhad Ali

2013-01-01

on free convection unsteady magnetohydrodynamic (MHD flow of viscous fluid embedded in a porous medium is presented. The flow in the fluid is induced due to uniform motion of the plate. The dimensionless coupled linear partial differential equations are solved by using Laplace transform method. The solutions that have been obtained are expressed in simple forms in terms of elementary function exp(· and complementary error function erfc(·. They satisfy the governing equations; all imposed initial and boundary conditions and can immediately be reduced to their limiting solutions. The influence of various embedded flow parameters such as the Hartmann number, permeability parameter, Grashof number, dimensionless time, Prandtl number, chemical reaction parameter, Schmidt number, and Soret number is analyzed graphically. Numerical solutions for skin friction, Nusselt number, and Sherwood number are also obtained in tabular forms.

Simulation of droplet impact onto a deep pool for large Froude numbers in different open-source codes

Science.gov (United States)

Korchagova, V. N.; Kraposhin, M. V.; Marchevsky, I. K.; Smirnova, E. V.

2017-11-01

A droplet impact on a deep pool can induce macro-scale or micro-scale effects like a crown splash, a high-speed jet, formation of secondary droplets or thin liquid films, etc. It depends on the diameter and velocity of the droplet, liquid properties, effects of external forces and other factors that a ratio of dimensionless criteria can account for. In the present research, we considered the droplet and the pool consist of the same viscous incompressible liquid. We took surface tension into account but neglected gravity forces. We used two open-source codes (OpenFOAM and Gerris) for our computations. We review the possibility of using these codes for simulation of processes in free-surface flows that may take place after a droplet impact on the pool. Both codes simulated several modes of droplet impact. We estimated the effect of liquid properties with respect to the Reynolds number and Weber number. Numerical simulation enabled us to find boundaries between different modes of droplet impact on a deep pool and to plot corresponding mode maps. The ratio of liquid density to that of the surrounding gas induces several changes in mode maps. Increasing this density ratio suppresses the crown splash.

An improved method to experimentally determine temperature and pressure behind laser-induced shock waves at low Mach numbers

International Nuclear Information System (INIS)

Hendijanifard, Mohammad; Willis, David A

2011-01-01

Laser-matter interactions are frequently studied by measuring the propagation of shock waves caused by the rapid laser-induced material removal. An improved method for calculating the thermo-fluid parameters behind shock waves is introduced in this work. Shock waves in ambient air, induced by pulsed Nd : YAG laser ablation of aluminium films, are measured using a shadowgraph apparatus. Normal shock solutions are applied to experimental data for shock wave positions and used to calculate pressure, temperature, and velocity behind the shock wave. Non-dimensionalizing the pressure and temperature with respect to the ambient values, the dimensionless pressure and temperature are estimated to be as high as 90 and 16, respectively, at a time of 10 ns after the ablation pulse for a laser fluence of F = 14.5 J cm -2 . The results of the normal shock solution and the Taylor-Sedov similarity solution are compared to show that the Taylor-Sedov solution under-predicts pressure when the Mach number of the shock wave is small. At a fluence of 3.1 J cm -2 , the shock wave Mach number is less than 3, and the Taylor-Sedov solution under-predicts the non-dimensional pressure by as much as 45%.

Dosage-based parameters for characterization of puff dispersion results.

Science.gov (United States)

Berbekar, Eva; Harms, Frank; Leitl, Bernd

2015-01-01

A set of parameters is introduced to characterize the dispersion of puff releases based on the measured dosage. These parameters are the dosage, peak concentration, arrival time, peak time, leaving time, ascent time, descent time and duration. Dimensionless numbers for the scaling of the parameters are derived from dimensional analysis. The dimensionless numbers are tested and confirmed based on a statistically representative wind tunnel dataset. The measurements were carried out in a 1:300 scale model of the Central Business District in Oklahoma City. Additionally, the effect of the release duration on the puff parameters is investigated. Copyright © 2014 Elsevier B.V. All rights reserved.

A Note on Variable Viscosity and Chemical Reaction Effects on Mixed Convection Heat and Mass Transfer Along a Semi-Infinite Vertical Plate

Directory of Open Access Journals (Sweden)

Mostafa A. A. Mahmoud

2007-01-01

Full Text Available In the present study, an analysis is carried out to study the variable viscosity and chemical reaction effects on the flow, heat, and mass transfer characteristics in a viscous fluid over a semi-infinite vertical porous plate. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by using the shooting method. The effects of different parameters on the dimensionless velocity, temperature, and concentration profiles are shown graphically. In addition, tabulated results for the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are presented and discussed.

Determination of the macroscopic chloride diffusivity in cementitious by porous materials coupling periodic homogenization of Nernst-Planck equation with experimental protocol

Directory of Open Access Journals (Sweden)

Olivier Millet

2008-03-01

Full Text Available In this paper, we propose a macroscopic migration model for cementitious porous media obtained from periodic homogenization technique. The dimensional analysis of Nernst-Planck equation leads to dimensionless numbers characterizing the problem. According to the order of magnitude of the dimensionless numbers, the homogenization of Nernst-Planck equation leads at the leading order to a macroscopic model where several rates can be coupled or not. For a large applied electrical field accelerating the transfer of ionic species, we obtain a macroscopic model only involving migration. A simple experimental procedure of measurement of the homogenized chlorides diffusivity is then proposed for cement-based materials.

Influence of yield stress on free convective boundary-layer flow of a non-Newtonian nanofluid past a vertical plate in a porous medium

International Nuclear Information System (INIS)

Hady, F. M.; Ibrahim, F. S.; Abdel-Gaied, S. M.; Eid, M. R.

2011-01-01

The effect of yield stress on the free convective heat transfer of dilute liquid suspensions of nanofluids flowing on a vertical plate saturated in porous medium under laminar conditions is investigated considering the nanofluid obeys the mathematical model of power-law. The model used for non-Newtonian nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing boundary- layer equations are cast into dimensionless system which is solved numerically using a deferred correction technique and Newton iteration. This solution depends on yield stress parameter Ω, a power-law index n, Lewis number Le, a buoyancy-ratio number Nr, a Brownian motion number Nb, and a thermophoresis number Nt. Analyses of the results found that the reduced Nusselt and Sherwood numbers are decreasing functions of the higher yield stress parameter for each dimensionless numbers, n and Le, except the reduced Sherwood number is an increasing function of higher Nb for different values of yield stress parameter

Correlation of Water Frost Porosity in Laminar Flow over Flat Surfaces

Science.gov (United States)

Kandula, Max

2011-01-01

A dimensionless correlation has been proposed for water frost porosity expressing its dependence on frost surface temperature and Reynolds number for laminar forced flow over a flat surface. The correlation is presented in terms of a dimensionless frost surface temperature scaled with the cold plate temperature, and the freezing temperature. The flow Reynolds number is scaled with reference to the critical Reynolds number for laminar-turbulent transition. The proposed correlation agrees satisfactorily with the simultaneous measurements of frost density and frost surface temperature covering a range of plate temperature, ambient air velocity, humidity, and temperature. It is revealed that the frost porosity depends primarily on the frost surface and the plate temperatures and the flow Reynolds number, and is only weakly dependent on the relative humidity. The results also point out the general character of frost porosity displaying a decrease with an increase in flow Reynolds number.

Inspection of the dynamic properties of laminar separation bubbles: free-stream turbulence intensity effects for different Reynolds numbers

Science.gov (United States)

Simoni, Daniele; Lengani, Davide; Ubaldi, Marina; Zunino, Pietro; Dellacasagrande, Matteo

2017-06-01

The effects of free-stream turbulence intensity (FSTI) on the transition process of a pressure-induced laminar separation bubble have been studied for different Reynolds numbers (Re) by means of time-resolved (TR) PIV. Measurements have been performed along a flat plate installed within a double-contoured test section, designed to produce an adverse pressure gradient typical of ultra-high-lift turbine blade profiles. A test matrix spanning 3 FSTI levels and 3 Reynolds numbers has been considered allowing estimation of cross effects of these parameters on the instability mechanisms driving the separated flow transition process. Boundary layer integral parameters, spatial growth rate and saturation level of velocity fluctuations are discussed for the different cases in order to characterize the base flow response as well as the time-mean properties of the Kelvin-Helmholtz instability. The inspection of the instantaneous velocity vector maps highlights the dynamics of the large-scale structures shed near the bubble maximum displacement, as well as the low-frequency motion of the fore part of the separated shear layer. Proper Orthogonal Decomposition (POD) has been implemented to reduce the large amount of data for each condition allowing a rapid evaluation of the group velocity, spatial wavelength and dominant frequency of the vortex shedding process. The dimensionless shedding wave number parameter makes evident that the modification of the shear layer thickness at separation due to Reynolds number variation mainly drives the length scale of the rollup vortices, while higher FSTI levels force the onset of the shedding phenomenon to occur upstream due to the higher velocity fluctuations penetrating into the separating boundary layer.

Thermal radiation and mass transfer effects on unsteady MHD free convection flow past a vertical oscillating plate

Science.gov (United States)

Rana, B. M. Jewel; Ahmed, Rubel; Ahmmed, S. F.

2017-06-01

Unsteady MHD free convection flow past a vertical porous plate in porous medium with radiation, diffusion thermo, thermal diffusion and heat source are analyzed. The governing non-linear, partial differential equations are transformed into dimensionless by using non-dimensional quantities. Then the resultant dimensionless equations are solved numerically by applying an efficient, accurate and conditionally stable finite difference scheme of explicit type with the help of a computer programming language Compaq Visual Fortran. The stability and convergence analysis has been carried out to establish the effect of velocity, temperature, concentration, skin friction, Nusselt number, Sherwood number, stream lines and isotherms line. Finally, the effects of various parameters are presented graphically and discussed qualitatively.

Analysis of heat transfer for unsteady MHD free convection flow of rotating Jeffrey nanofluid saturated in a porous medium

Directory of Open Access Journals (Sweden)

Nor Athirah Mohd Zin

Full Text Available In this article, the influence of thermal radiation on unsteady magnetohydrodynamics (MHD free convection flow of rotating Jeffrey nanofluid passing through a porous medium is studied. The silver nanoparticles (AgNPs are dispersed in the Kerosene Oil (KO which is chosen as conventional base fluid. Appropriate dimensionless variables are used and the system of equations is transformed into dimensionless form. The resulting problem is solved using the Laplace transform technique. The impact of pertinent parameters including volume fraction φ, material parameters of Jeffrey fluid λ1, λ, rotation parameter r, Hartmann number Ha, permeability parameter K, Grashof number Gr, Prandtl number Pr, radiation parameter Rd and dimensionless time t on velocity and temperature profiles are presented graphically with comprehensive discussions. It is observed that, the rotation parameter, due to the Coriolis force, tends to decrease the primary velocity but reverse effect is observed in the secondary velocity. It is also observed that, the Lorentz force retards the fluid flow for both primary and secondary velocities. The expressions for skin friction and Nusselt number are also evaluated for different values of emerging parameters. A comparative study with the existing published work is provided in order to verify the present results. An excellent agreement is found. Keywords: Jeffrey nanofluid, AgNPs, MHD and Porosity, Rotating flow, Laplace transform technique

A modified variable physical properties model, for analyzing nanofluids flow and heat transfer over nonlinearly stretching sheet

Directory of Open Access Journals (Sweden)

Pooria Akbarzadeh

2017-07-01

Full Text Available In this paper, the problem of laminar nanofluid flow which results from the nonlinear stretching of a flat sheet is investigated numerically. In this paper, a modified variable physical properties model for analyzing nanofluids flow and heat transfer is introduced. In this model, the effective viscosity, density, and thermal conductivity of the solid-liquid mixture (nanofluids which are commonly utilized in the homogenous single-phase model, are locally combined with the prevalent single-phase model. A numerical similarity solution is considered which depends on the local Prandtl number, local Brownian motion number, local Lewis number, and local thermophoresis number. The results are compared to the prevalent single-phase model. This comparison depicts that the prevalent single-phase model has a considerable deviation for predicting the behavior of nanofluids flow especially in dimensionless temperature and nanoparticle volume fraction. In addition the effect of the governing parameters such as Prandtl number, the Brownian motion number, the thermophoresis parameter, the Lewis number, and etc. on the velocity, temperature, and volume fraction distribution and the dimensionless heat and mass transfer rates are examined.

Mixed Convection Heat Transfer on the Outside of a Vertical Cylinder

Energy Technology Data Exchange (ETDEWEB)

Bhattacharyya, A

1965-10-15

An experimental study was made of turbulent heat transfer from a vertical cylinder placed in a square channel. The flow medium was water flowing upwards. Basic differential equations governing the mixed flow heat transfer phenomena in a vertical annulus are presented. A dimensional analysis is done to find the dimensionless variables affecting the relative magnitude of the effect of buoyancy on forced convection heat transfer. Dimensionless equations correlating the experimental data ana incorporating a buoyancy parameter of the form Gr/Re{sup 2} are presented. Reynolds number range covered is 690 to 129,500 and the Rayleigh num- ber range covered is 10{sup 9} to 4.2 x 10{sup 13} . Effect of different length parameters, like hydraulic diameter and distance of the measuring point from the inlet of the test section, on dimensionless equations are studied.

A theoretical study on the accuracy of the T-history method for enthalpy–temperature curve measurement: analysis of the influence of thermal gradients inside T-history samples

International Nuclear Information System (INIS)

Mazo, Javier; Delgado, Mónica; Lázaro, Ana; Dolado, Pablo; Peñalosa, Conchita; Marín, José María; Zalba, Belén

2015-01-01

The present work analyses the effect of radial thermal gradients inside T-history samples on the enthalpy temperature curve measurement. A conduction heat transfer model has been utilized for this purpose. Some expressions have been obtained that relate the main dimensionless numbers of the experiments with the deviations in specific heat capacity, phase change enthalpy and phase change temperature estimations. Although these relations can only be strictly applied to solid materials (e.g. measurements of shape stabilized phase change materials), they can provide some useful and conservative bounds for the deviations of the T-history method. Biot numbers emerge as the most relevant dimensionless parameters in the accuracy of the specific heat capacity and phase change enthalpy estimation whereas this model predicts a negligible influence of the temperature levels used for the experiments or the Stefan number. (paper)

A thermodynamic analysis of non-equilibrium heat conduction in a semi-infinite medium subjected to a step change in temperature

Energy Technology Data Exchange (ETDEWEB)

Hussain, A.K.; Hussain, T.A.; Shahad, Haroun A.K. [Babylon Univ., Dept. of Mechanical Engineering, Babylon (Iraq)

2003-05-01

The problem of non-equilibrium heat conduction in a semi-infinite medium subjected to a step change in temperature is analyzed thermodynamically using the extended irreversible thermodynamic approach. The results show clearly the wave nature of the dimensionless temperature distribution, Stanton number and the dimensionless entropy change profiles. The non-equilibrium profiles approach the equilibrium profiles as the speed of wave propagation is increased. The results also show that the non-equilibrium temperature is higher than the equilibrium temperature but the difference decreases as the wave propagation speed increases. (Author)

Entropy analysis of convective MHD flow of third grade non-Newtonian fluid over a stretching sheet

Directory of Open Access Journals (Sweden)

M.M. Rashidi

2017-03-01

Full Text Available The purpose of this article is to study and analyze the convective flow of a third grade non-Newtonian fluid due to a linearly stretching sheet subject to a magnetic field. The dimensionless entropy generation equation is obtained by solving the reduced momentum and energy equations. The momentum and energy equations are reduced to a system of ordinary differential equations by a similarity method. The optimal homotopy analysis method (OHAM is used to solve the resulting system of ordinary differential equations. The effects of the magnetic field, Biot number and Prandtl number on the velocity component and temperature are studied. The results show that the thermal boundary-layer thickness gets decreased with increasing the Prandtl number. In addition, Brownian motion plays an important role to improve thermal conductivity of the fluid. The main purpose of the paper is to study the effects of Reynolds number, dimensionless temperature difference, Brinkman number, Hartmann number and other physical parameters on the entropy generation. These results are analyzed and discussed.

Stability of a radial immiscible drive

Energy Technology Data Exchange (ETDEWEB)

Bataille, J

1968-11-01

The stability of the displacement front between 2 immiscible fluids of radial flow between 2 parallel plates (Hele-Shaw model) is studied mathematically by superposing onto the circular displacement front a sinusoidal perturbation. The equations are reduced to dimensionless variables, and it is shown that the stable and unstable domains in a plot: dimensionless viscosity vs. dimensionless time are separated by a polygonal contour, each side of the contour being characterized by the (integer) number of perturbations along the circumference. There is a critical reduced time below which the perturbations are amortized but beyond which they are amplified. Experimental results have been in fair general agreement with theoretical results, the divergence between them being attributable to neglecting capillary phenomena, which may become very important at large radial distances. One test with miscible fluids has shown that even in this case, there is a critical time or an equivalent critical radius.

Transient heat characteristics of water-saturated porous media with freezing; Toketsu wo tomonau gansui takoshitsu sonai no hiteijo netsu tokusei

Energy Technology Data Exchange (ETDEWEB)

Sasaki, A [Akita National College of Technology, Akita (Japan)

1998-02-25

Analytical and experimental investigations were performed to examine the transient heat characteristics of water-saturated porous media with freezing. As a physical model, a two-dimensional vertical cavity was considered. One vertical wall was abruptly cooled below the fusion temperature. Other three walls were thermally insulated. Three different sizes of glass, and iron, alumina and copper beads were used as the porous media in this study. The cold energy stored up in the porous media and the average thickness of frozen layer were measured in the experiments. Comparisons of the analytical results with the experimental ones were made, and the effects of Darcy number, Stefan number and modified Prandtl number on the transient heat characteristics were discussed. The dimensionless equations for predicting the averaged frozen layer thickness and the stored cold energy were obtained as a function of various dimensionless parameters. 8 refs., 16 figs., 1 tab.

Influence of non-integer order parameter and Hartmann number on the heat and mass transfer flow of a Jeffery fluid over an oscillating vertical plate via Caputo-Fabrizio time fractional derivatives

Science.gov (United States)

Butt, A. R.; Abdullah, M.; Raza, N.; Imran, M. A.

2017-10-01

In this work, semi analytical solutions for the heat and mass transfer of a fractional MHD Jeffery fluid over an infinite oscillating vertical plate with exponentially heating and constant mass diffusion via the Caputo-Fabrizio fractional derivative are obtained. The governing equations are transformed into dimensionless form by introducing dimensionless variables. A modern definition of the Caputo-Fabrizio derivative has been used to develop the fractional model for a Jeffery fluid. The expressions for temperature, concentration and velocity fields are obtained in the Laplace transformed domain. We have used the Stehfest's and Tzou's algorithm for the inverse Laplace transform to obtain the semi analytical solutions for temperature, concentration and velocity fields. In the end, in order to check the physical impact of flow parameters on temperature, concentration and velocity fields, results are presented graphically and in tabular forms.

Parametric Studies of Flat Plate Trajectories Using VIC and Penalization

Directory of Open Access Journals (Sweden)

François Morency

2018-01-01

Full Text Available Flying debris is generated in several situations: when a roof is exposed to a storm, when ice accretes on rotating wind turbines, or during inflight aircraft deicing. Four dimensionless parameters play a role in the motion of flying debris. The goal of the present paper is to investigate the relative importance of four dimensionless parameters: the Reynolds number, the Froude number, the Tachikawa number, and the mass moment of inertia parameters. Flying debris trajectories are computed with a fluid-solid interaction model formulated for an incompressible 2D laminar flow. The rigid moving solid effects are modelled in the Navier-Stokes equations using penalization. A VIC scheme is used to solve the flow equations. The aerodynamic forces and moments are used to compute the acceleration and the velocity of the solid. A database of 64 trajectories is built using a two-level full factorial design for the four factors. The dispersion of the plate position at a given horizontal position decreases with the Froude number. Moreover, the Tachikawa number has a significant effect on the median plate position.

Non-Darcy Mixed Convection in a Doubly Stratified Porous Medium with Soret-Dufour Effects

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D. Srinivasacharya

2014-01-01

Full Text Available This paper presents the nonsimilarity solutions for mixed convection heat and mass transfer along a semi-infinite vertical plate embedded in a doubly stratified fluid saturated porous medium in the presence of Soret and Dufour effects. The flow in the porous medium is described by employing the Darcy-Forchheimer based model. The nonlinear governing equations and their associated boundary conditions are initially cast into dimensionless forms and then solved numerically. The influence of pertinent parameters on dimensionless velocity, temperature, concentration, heat, and mass transfer in terms of the local Nusselt and Sherwood numbers is discussed and presented graphically.

Numerical study of free convection in an enclosure with two vertical isothermal walls

International Nuclear Information System (INIS)

Barletta, A.; Rossi di Schio, E.; Zanchini, E.; Nobile, E.; Pinto, F.

2005-01-01

In this paper, natural convection is studied in a 2D-cavity with two vertical isothermal walls, kept at different temperatures, and two adiabatic walls which are either straight (rectangular cavity) or elliptic (modified rectangular cavity). The local mass, momentum and energy balance equations are written in a dimensionless form and solved numerically, by means of two different software packages based on Galerkin finite element methods. With reference to a Prandtl number of 0.71, two rectangular cavities are studied: a square one and a cavity with height double than width. Then, for each value of the ratio between height and width, two cavities with elliptic boundaries are investigated. The numerical solution shows that the elliptic boundaries enhance the mean Nusselt number and the dimensionless mean kinetic energy of the fluid. (authors)

Implications of fin profiles on overall performance and weight reduction of a fin and tube heat exchanger

DEFF Research Database (Denmark)

Singh, Shobhana; Sørensen, Kim; Simonsen, Anders Schou

2017-01-01

Fin and tube heat exchangers are being used in several industrial applications by means of novel design and optimized performance. Improvements in geometric design may deliver energy efficient and cost-effective heat exchanger performance with reduced weight. In this paper, a systematic study...... on a cross-flow type fin and tube heat exchanger design for a waste heat recovery application is conducted. The geometric profile of the fin is characterized by a dimensionless design variable named aspect ratio which is parametrically varied to obtain different profiles. Two cases, case-I, and case......,000 using computational fluid dynamics. The numerical results obtained for the reference fin profile are verified with the experimental correlations. Dimensionless parameters such as Nusselt number, Euler number, and efficiency index are calculated to predict the overall performance of the heat exchanger...

Propagation of laser-generated plasma jet in an ambient medium

International Nuclear Information System (INIS)

Loupias, B; Falize, E; Vinci, T; Bouquet, S; Gregory, C D; Koenig, M; Ravasio, A; Pikuz, S; Waugh, J; Woolsey, N C; Nazarov, W; Michaut, C; Kuramitsu, Y; Seiichi, D; Sakawa, Y; Takabe, H; Schiavi, A; Atzeni, S

2009-01-01

In this work we present experimental research related to laboratory astrophysics using an intense laser. The goal of these experiments is to investigate some of the complex features of young stellar objects and astrophysical outflows, in particular the plasma jet interaction with the interstellar medium. The relevance of these experiments to astrophysics is measured through similarity criteria (scaling laws). These ensure the similarity between the astrophysical object and the laboratory provided that the dimensionless numbers are equivalent. Consequently, measurements of the plasma parameters are crucial to link laboratory research to astrophysics as they are needed for the determination of these dimensionless numbers. In this context, we designed experiments to generate plasma jets using an intense laser, and to study the evolution in vacuum and in an ambient medium.

An inequality relating gauge group coupling constants and the number of generations in a string inspired model

International Nuclear Information System (INIS)

Nielsen, H.B.; Bennett, D.L.

1987-12-01

Using a model with a regularized (e.g. latticized) Kaluza-Klein space-time at the fundamental scale with Yang-Mills fields in the compactified dimensions, we examine the β-function for a dimensionless expression for the coupling constants g in D-dimensions. In going from the Planck scale of D > 4 down in energy to the scale where D goes from D > 4 to D = 4, it is argued that couplings are weakened by a factor roughly equal to the number of fundamental string regions that can be accommadated in the volume of the compactification space. Subsequently this factor is claimed to be greater than the number of generations by using an argument reminiscent of that often encountered in string model T.O.E. in which various quark and lepton generations are said to correspond to various zero modes of a Weyl operator in the compactifying space. Finally, it is argued that the inequality, which can be shown to be more saturated the larger the gauge group, is already near saturation for the group factors of the SMG. This fact leads to several conclusions: 1. there is not room for many more than 3 generations; 2. G.U.T. can be accommadated only at scales very close to the fundamental scale; 3. No new blossoms are expected to be found in the desert; 4. the compactifying space should not be 'larger than necessary'; 5. at the fundamental scale, couplings are expected to be close to (but not suspiciousely close to) β crit. . (orig./HSI)

A mechanism of thrust enhancement on a heaving plate due to flexibility at moderately low Reynolds numbers

Science.gov (United States)

Lin, Yung-Sheng; Tzeng, Yau-Ting; Chang, Chien-Cheng; Chu, Chin-Chou

2017-11-01

A numerical study is conducted to investigate the force mechanisms for a 3D heaving flexible plate from the perspective of a diagnostic force element analysis (Chang 1992). The problem is relevant to a simplified flapping fish-tail with the front edge held fixed in space. The flow is assumed to be laminar with the Reynolds numbers fixed at Re =200 or 500, and the Strouhal number St ranging from 0.1 to 0.6, and the flexure amplitude of the plate a0 for 0.1 to 0.25 (dimensionless). It is shown that heaving, whilst increasing thrust generation, also reduces the frictional drag, yet the flexibility promotes thrust generation at the expense of accruing more frictional drag. In the literature, the thrust exerted on the tail-mimicking plate is largely credited to the vortices in the wake. However, this study performs a regional force analysis to show that the vorticity in the wake region supplies approximately 20-30% of the total thrust, especially in the cases of strong thrust generation. Comparable contributions come also from the regions direct above and below the heaving plate (mainly including the attached vortices) as well as from the two side regions (mainly including the tip vortices) next to the flapping plate. In addition, the potential motion associated with the unsteady flapping and the contribution from the surface vorticity are non-negligible constituent force components. MOST, TAIWAN under Contacts NO. 105-2221-E-002-097-MY3 and NO. 105-2221-E-002 -105 -MY3.

Investigating the Variability in Cumulus Cloud Number as a Function of Subdomain Size and Organization using large-domain LES

Science.gov (United States)

Neggers, R.

2017-12-01

Recent advances in supercomputing have introduced a "grey zone" in the representation of cumulus convection in general circulation models, in which this process is partially resolved. Cumulus parameterizations need to be made scale-aware and scale-adaptive to be able to conceptually and practically deal with this situation. A potential way forward are schemes formulated in terms of discretized Cloud Size Densities, or CSDs. Advantages include i) the introduction of scale-awareness at the foundation of the scheme, and ii) the possibility to apply size-filtering of parameterized convective transport and clouds. The CSD is a new variable that requires closure; this concerns its shape, its range, but also variability in cloud number that can appear due to i) subsampling effects and ii) organization in a cloud field. The goal of this study is to gain insight by means of sub-domain analyses of various large-domain LES realizations of cumulus cloud populations. For a series of three-dimensional snapshots, each with a different degree of organization, the cloud size distribution is calculated in all subdomains, for a range of subdomain sizes. The standard deviation of the number of clouds of a certain size is found to decrease with the subdomain size, following a powerlaw scaling corresponding to an inverse-linear dependence. Cloud number variability also increases with cloud size; this reflects that subsampling affects the largest clouds first, due to their typically larger neighbor spacing. Rewriting this dependence in terms of two dimensionless groups, by dividing by cloud number and cloud size respectively, yields a data collapse. Organization in the cloud field is found to act on top of this primary dependence, by enhancing the cloud number variability at the smaller sizes. This behavior reflects that small clouds start to "live" on top of larger structures such as cold pools, favoring or inhibiting their formation (as illustrated by the attached figure of cloud mask

Analytical interpretation of the local thermal non-equilibrium condition of porous media imbedded in tube heat exchangers

International Nuclear Information System (INIS)

Dehghan, Maziar; Jamal-Abad, Milad Tajik; Rashidi, Saman

2014-01-01

Highlights: • The Brinkman–Forchheimer–Darcy equation is solved using the perturbation methods. • Temperature profile is obtained analytically using the successive approx. method. • A new dimensionless number representing the intensity of LTNE is presented. • The LENT intensity is proportional to the product of velocity and temperature. • Effects of Da number, porosity of medium, and conductivity ratio are investigated. - Abstract: Local thermal non-equilibrium (LTNE) effects in the developed region of the forced convection in a circular tube filled with saturated porous medium are analytically studied at the constant wall-temperature boundary condition, as well as at the iso-flux boundary condition. The flow in the pipe is described by the Brinkman-Forchheimer-extended Darcy equation. A two-equation model is used for the energy balance. Profiles describing the velocity field obtained by perturbation techniques are used to find the temperature distributions using the successive approximation method. Moreover, the velocity and temperature fields are simulated numerically to validate the results of the analytical part. A fundamental relation and a new dimensionless number, ΔNE, for the temperature difference between the fluid and solid phases (LTNE intensity) are established based on a perturbation analysis. It is found that the LTNE intensity (ΔNE) is proportional to the product of the normalized velocity and the dimensionless temperature at LTE condition and depends on the conductivity ratio, Darcy number, and the porosity of the medium. Finally, the proposed relation for the LTNE intensity is simple and fundamental for estimation of the importance of LTNE condition

THEORETICAL AND EXPERIMENTAL ANALYSIS OF A CROSS-FLOW HEAT EXCHANGER

Directory of Open Access Journals (Sweden)

R. Tuğrul OĞULATA

1996-03-01

Full Text Available In this study, cross-flow plate type heat exchanger has been investigated because of its effective use in waste heat recovery systems. For this purpose, a heat regain system has been investigated and manufactured in laboratory conditions. Manufactured heat exchanger has been tested with an applicable experimental set up and temperatures, velocity of the air and the pressure losses occuring in the system have been measured and the efficiency of the system has been determined. The irreversibility of heat exchanger has been taken into consideration while the design of heat exchanger is being performed. So minimum entropy generation number has been analysied with respect to second law of thermodynamics in cross-flow heat exchanger. The minimum entropy generation number depends on parameters called optimum flow path length, dimensionless mass velocity and dimensionless heat transfer area. Variations of entropy generation number with these parameters have been analysied and introduced their graphics with their comments.

Rewetting of composite slab

International Nuclear Information System (INIS)

Satapathy, A.K.; Singh, K.C.

1996-01-01

The process of re-establishment of wetting of hot surface is of practical importance in chemical, metallurgical and nuclear industries. Rewetting is considered in emergency core cooling in nuclear reactors in the event of postulated loss of coolant accident (LOCA). This paper deals with numerical solution of the two-dimensional quasi-static conduction controlled rewetting of an infinite parallel sided composite slab assuming perfect contact is maintained at the interface. On the wetted side upstream of the quench front, a constant heat transfer coefficient is assumed. The downstream of quench front and unwetted side of slab are supposed to be adiabatic. The solution gives the quench front temperature as a function of various model parameters such as Peclet number, wet side Blot number, dimensionless thickness of slab and cladding to fuel ratio of thermal conductivities. The results show that for large values of rewetting velocities, the dimensionless rewetting temperature is unaffected by fuel properties for all values of Blot numbers. (author). 7 refs., 2 tabs., 1 fig

A methodology to predict the uniformity of double-shell waste slurries based on mixer pump operation

International Nuclear Information System (INIS)

Liljegren, L.M.; Bamberger, J.A.

1992-08-01

Dimensional analysis is used to determine the similarity parameters that describe the uniformity of radioactive slurry wastes to be suspended by mixer pumps. The results of this analysis are applied to the design of scaled experiments that will determine the operating parameters that will ensure an adequately uniform feed stream during waste retrieval from Hanford double-shell tanks. Ten dimensionless parameters describing the slurry mixing process were identified. Of these, three describe purely geometric features, three describe slurry properties only, one is a dimensionless time scale, and three describe important dynamic factors. The three parameters describing the dynamic features are the Reynolds number, which describes the degree of turbulence in the tank; the Froude number, which describes the effects of stratification on the circulation patterns; and the gravitational settling number, which describes the balance between the work done by gravity to cause settling and the work done by the pump to resuspend particles

The Influence of Cross-Sectional Shape and Orientation of Micropillar Surface on Microdroplet Formation by a Dewetting Process

Directory of Open Access Journals (Sweden)

Bambang Arip Dwiyantoro

2013-07-01

Full Text Available In this study the dewetting process on micropillars of three different cross-sectional shapes, i.e. circular, square and triangular, was numerically investigated. The influence of the orientation of the triangular and square micropillars on the dewetting behavior was also studied. The numerical simulations showed that the cross-sectional shapes of the micropillars and their orientation play an important role in determining the flow pattern of the dewetting process, especially the evolution and movement of the meniscus across the micropillar before a microdroplet is formed. The diameter of the microdroplets is mainly determined by the capillary effect, viscous drag and fluid inertia contributed by the peeling rate and the thickness of the water layer above the micropillar. The numerical results also indicate that the hydraulic diameter of the micropillars (Dp is one of the parameters governing the size of the microdroplets formed on the top surface of the micropillars after the dewetting process, while the microdroplet diameter is almost insensitive to the cross-sectional shape and orientation of the micropillars. The dimensionless diameter of the microdroplets (d can then be expressed as a function of a dimensionless group, i.e. the Ohnesorge number (Oh, the capillary number (Ca, the dimensionless liquid thickness (H, and the contact angle (q.

Improved lumped models for transient combined convective and radiative cooling of multi-layer composite slabs

International Nuclear Information System (INIS)

An Chen; Su Jian

2011-01-01

Improved lumped parameter models were developed for the transient heat conduction in multi-layer composite slabs subjected to combined convective and radiative cooling. The improved lumped models were obtained through two-point Hermite approximations for integrals. Transient combined convective and radiative cooling of three-layer composite slabs was analyzed to illustrate the applicability of the proposed lumped models, with respect to different values of the Biot numbers, the radiation-conduction parameter, the dimensionless thermal contact resistances, the dimensionless thickness, and the dimensionless thermal conductivity. It was shown by comparison with numerical solution of the original distributed parameter model that the higher order lumped model (H 1,1 /H 0,0 approximation) yielded significant improvement of average temperature prediction over the classical lumped model. In addition, the higher order (H 1,1 /H 0,0 ) model was applied to analyze the transient heat conduction problem of steel-concrete-steel sandwich plates. - Highlights: → Improved lumped models for convective-radiative cooling of multi-layer slabs were developed. → Two-point Hermite approximations for integrals were employed. → Significant improvement over classical lumped model was achieved. → The model can be applied to high Biot number and high radiation-conduction parameter. → Transient heat conduction in steel-concrete-steel sandwich pipes was analyzed as an example.

Instability and associated roll structure of Marangoni convection in high Prandtl number liquid bridge with large aspect ratio

Science.gov (United States)

Yano, T.; Nishino, K.; Kawamura, H.; Ueno, I.; Matsumoto, S.

2015-02-01

This paper reports the experimental results on the instability and associated roll structures (RSs) of Marangoni convection in liquid bridges formed under the microgravity environment on the International Space Station. The geometry of interest is high aspect ratio (AR = height/diameter ≥ 1.0) liquid bridges of high Prandtl number fluids (Pr = 67 and 207) suspended between coaxial disks heated differentially. The unsteady flow field and associated RSs were revealed with the three-dimensional particle tracking velocimetry. It is found that the flow field after the onset of instability exhibits oscillations with azimuthal mode number m = 1 and associated RSs traveling in the axial direction. The RSs travel in the same direction as the surface flow (co-flow direction) for 1.00 ≤ AR ≤ 1.25 while they travel in the opposite direction (counter-flow direction) for AR ≥ 1.50, thus showing the change of traveling directions with AR. This traveling direction for AR ≥ 1.50 is reversed to the co-flow direction when the temperature difference between the disks is increased to the condition far beyond the critical one. This change of traveling directions is accompanied by the increase of the oscillation frequency. The characteristics of the RSs for AR ≥ 1.50, such as the azimuthal mode of oscillation, the dimensionless oscillation frequency, and the traveling direction, are in reasonable agreement with those of the previous sounding rocket experiment for AR = 2.50 and those of the linear stability analysis of an infinite liquid bridge.

Thermodynamic optimization of ground heat exchangers with single U-tube by entropy generation minimization method

International Nuclear Information System (INIS)

Li Min; Lai, Alvin C.K.

2013-01-01

Highlights: ► A second-law-based analysis is performed for single U-tube ground heat exchangers. ► Two expressions for the optimal length and flow velocity are developed for GHEs. ► Empirical velocities of GHEs are large compared to thermodynamic optimum values. - Abstract: This paper investigates thermodynamic performance of borehole ground heat exchangers with a single U-tube by the entropy generation minimization method which requires information of heat transfer and fluid mechanics, in addition to thermodynamics analysis. This study first derives an expression for dimensionless entropy generation number, a function that consists of five dimensionless variables, including Reynolds number, dimensionless borehole length, scale factor of pressures, and two duty parameters of ground heat exchangers. The derivation combines a heat transfer model and a hydraulics model for borehole ground heat exchangers with the first law and the second law of thermodynamics. Next, the entropy generation number is minimized to produce two analytical expressions for the optimal length and the optimal flow velocity of ground heat exchangers. Then, this paper discusses and analyzes implications and applications of these optimization formulas with two case studies. An important finding from the case studies is that widely used empirical velocities of circulating fluid are too large to operate ground-coupled heat pump systems in a thermodynamic optimization way. This paper demonstrates that thermodynamic optimal parameters of ground heat exchangers can probably be determined by using the entropy generation minimization method.

Numerical and dimensional analysis of nanoparticles transport with two-phase flow in porous media

KAUST Repository

El-Amin, Mohamed

2015-04-01

In this paper, a mathematical model and numerical simulation are developed to describe the imbibition of nanoparticles-water suspension into two-phase flow in a porous medium. The flow system may be changed from oil-wet to water-wet due to nanoparticles (which are also water-wet) deposition on surface of the pores. So, the model is extended to include the negative capillary pressure and mixed-wet relative permeability correlations to fit with the mixed-wet system. Moreover, buoyancy and capillary forces as well as Brownian diffusion and mechanical dispersion are considered in the mathematical model. An example of countercurrent imbibition in a core of small scale is considered. A dimensional analysis of the governing equations is introduced to examine contributions of each term of the model. Several important dimensionless numbers appear in the dimensionless equations, such as Darcy number Da, capillary number Ca, and Bond number Bo. Throughout this investigation, we monitor the changing of the fluids and solid properties due to addition of the nanoparticles using numerical experiments.

Heat-transfer correlations for natural convection boiling

International Nuclear Information System (INIS)

Stephan, K.; Abdelsalam, M.

1980-01-01

To-date there exists no comprehensive theory allowing the prediction of heat-transfer coefficients in natural convection boiling, in spite of the many efforts made in this field. In order to establish correlations with wide application, the methods of regression analysis were applied to the nearly 500 existing experimental data points for natural convection boiling heat transfer. As demonstrated by the analysis, these data can best be represented by subdividing the substances into four groups (water, hydrocarbons, cryogenic fluids and refrigerants) and employing a different set of dimensionless numbers for each group of substances, because certain dimensionless numbers important for one group of substances are unimportant to another. One equation valid for all substances could be built up, but its accuracy would be less than that obtained for the individual correlations without adding undesirable complexity. (author)

Sadhana | Indian Academy of Sciences

Indian Academy of Sciences (India)

Prandtl number and the dimensionless frequency of heating on flow formation and thermal behaviour are discussed with the aid of graphs. During the course of investigation, it is found that the oscillation amplitude of the friction factor is ...

Study on the phenomena of natural circulation in LMFBR

International Nuclear Information System (INIS)

Takeda, Hirofumi; Koga, Tomonari

1993-01-01

Decay heat removal with natural circulation is to be introduced to the LMFBR operation under loss of the electric power supply. The natural circulation is highly reliable, but the phenomenon is essentially unstable and subtle, which makes fine prediction difficult. The difficulties of experimental prediction are explained by facts that the phenomena are ruled by the delicate balance between the buoyancy force and the low pressure loss and are influenced by the various parameters such as local geometry, heat capacity and so on. Therefore the similarity rule for the natural circulation has not been fully understood. This study has been conducted to establish the simulation method for the natural circulation phenomena and the detailed phenomena have been reviewed. For the natural circulation in an LMFBR plant, there are no readily available reference velocity and temperature. These values are related only with the heating and cooling rate, the characteristic length and physical properties of the testing fluid. Basic equations were transformed by these values, and dimensionless equations were derived and then two dimensionless numbers, the Gr' number and the Bo' number, were identified. In order to examine the similarity rule for natural circulation we performed experiments using the different scale water models, a 1/20th and a 1/6th model. The temperatures and velocities at typical points were measured in the transient condition with various heating rate as a parameter. Measured temperatures and velocities were transformed to dimensionless forms for comparison and the effects of the Bo' number and the Gr' number were examined. As a result, it was clarified that the effect of the Gr' number is negligibly small but the effect of Bo' number still remained in our experimental range. The Bo' number of an actual plant is within the range of this experiment. Accordingly similitude of the Bo' number becomes important in an experiment to simulate an actual plant. (author)

Reynolds analogy for the Rayleigh problem at various flow modes.

Science.gov (United States)

Abramov, A A; Butkovskii, A V

2016-07-01

The Reynolds analogy and the extended Reynolds analogy for the Rayleigh problem are considered. For a viscous incompressible fluid we derive the Reynolds analogy as a function of the Prandtl number and the Eckert number. We show that for any positive Eckert number, the Reynolds analogy as a function of the Prandtl number has a maximum. For a monatomic gas in the transitional flow regime, using the direct simulation Monte Carlo method, we investigate the extended Reynolds analogy, i.e., the relation between the shear stress and the energy flux transferred to the boundary surface, at different velocities and temperatures. We find that the extended Reynolds analogy for a rarefied monatomic gas flow with the temperature of the undisturbed gas equal to the surface temperature depends weakly on time and is close to 0.5. We show that at any fixed dimensionless time the extended Reynolds analogy depends on the plate velocity and temperature and undisturbed gas temperature mainly via the Eckert number. For Eckert numbers of the order of unity or less we generalize an extended Reynolds analogy. The generalized Reynolds analogy depends mainly only on dimensionless time for all considered Eckert numbers of the order of unity or less.

Application of dimensionless sediment rating curves to predict suspended-sediment concentrations, bedload, and annual sediment loads for rivers in Minnesota

Science.gov (United States)

Ellison, Christopher A.; Groten, Joel T.; Lorenz, David L.; Koller, Karl S.

2016-10-27

Consistent and reliable sediment data are needed by Federal, State, and local government agencies responsible for monitoring water quality, planning river restoration, quantifying sediment budgets, and evaluating the effectiveness of sediment reduction strategies. Heightened concerns about excessive sediment in rivers and the challenge to reduce costs and eliminate data gaps has guided Federal and State interests in pursuing alternative methods for measuring suspended and bedload sediment. Simple and dependable data collection and estimation techniques are needed to generate hydraulic and water-quality information for areas where data are unavailable or difficult to collect.The U.S. Geological Survey, in cooperation with the Minnesota Pollution Control Agency and the Minnesota Department of Natural Resources, completed a study to evaluate the use of dimensionless sediment rating curves (DSRCs) to accurately predict suspended-sediment concentrations (SSCs), bedload, and annual sediment loads for selected rivers and streams in Minnesota based on data collected during 2007 through 2013. This study included the application of DSRC models developed for a small group of streams located in the San Juan River Basin near Pagosa Springs in southwestern Colorado to rivers in Minnesota. Regionally based DSRC models for Minnesota also were developed and compared to DSRC models from Pagosa Springs, Colorado, to evaluate which model provided more accurate predictions of SSCs and bedload in Minnesota.Multiple measures of goodness-of-fit were developed to assess the effectiveness of DSRC models in predicting SSC and bedload for rivers in Minnesota. More than 600 dimensionless ratio values of SSC, bedload, and streamflow were evaluated and delineated according to Pfankuch stream stability categories of “good/fair” and “poor” to develop four Minnesota-based DSRC models. The basis for Pagosa Springs and Minnesota DSRC model effectiveness was founded on measures of goodness

The effect of Reynolds number on the propulsive efficiency of a biomorphic pulsed-jet underwater vehicle

International Nuclear Information System (INIS)

Moslemi, Ali A; Krueger, Paul S

2011-01-01

The effect of Reynolds number on the propulsive efficiency of pulsed-jet propulsion was studied experimentally on a self-propelled, pulsed-jet underwater vehicle, dubbed Robosquid due to the similarity of its propulsion system with squid. Robosquid was tested for jet slug length-to-diameter ratios (L/D) in the range 2-6 and dimensionless frequency (St L ) in the range 0.2-0.6 in a glycerin-water mixture. Digital particle image velocimetry was used for measuring the impulse and energy of jet pulses from the velocity and vorticity fields of the jet flow to calculate the pulsed-jet propulsive efficiency, and compare it with an equivalent steady jet system. Robosquid's Reynolds number (Re) based on average vehicle velocity and vehicle diameter ranged between 37 and 60. The current results for propulsive efficiency were compared to the previously published results in water where Re ranged between 1300 and 2700. The results showed that the average propulsive efficiency decreased by 26% as the average Re decreased from 2000 to 50 while the ratio of pulsed-jet to steady jet efficiency (η P /η P,ss ) increased up to 0.15 (26%) as the Re decreased over the same range and for similar pulsing conditions. The improved η P /η P,ss at lower Re suggests that pulsed-jet propulsion can be used as an efficient propulsion system for millimeter-scale propulsion applications. The Re = 37-60 conditions in the present investigation, showed a reduced dependence of η P and η P /η P,ss on L/D compared to higher Re results. This may be due to the lack of clearly observed vortex ring pinch-off as L/D increased for this Re regime.

THE PROCESS OF MASS TRANSFER ON THE SOLID-LIQUID BOUNDARY LAYER DURING THE RELEASE OF DICLOFENAC SODIUM AND PAPAVERINE HYDROCHLORIDE FROM TABLETS IN A PADDLE APPARATUS.

Science.gov (United States)

Kasperek, Regina; Zimmer, Lukasz; Poleszak, Ewa

2016-01-01

The release study of diclofenac sodium (DIC) and papaverine hydrochloride (PAP) from two formulations of the tablets in the paddle apparatus using different rotation speeds to characterize the process of mass transfer on the solid-liquid boundary layer was carried out. The dissolution process of active substances was described by values of mass transfer coefficients, the diffusion boundary layer thickness and dimensionless numbers (Sh and Re). The values of calculated parameters showed that the release of DIC and PAP from tablets comprising potato starch proceeded faster than from tablets containing HPMC and microcrystalline cellulose. They were obtained by direct dependencies between Sh and Re in the range from 75 rpm to 125 rpm for both substances from all tablets. The description of the dissolution process with the dimensionless numbers make it possible to plan the drug with the required release profile under given in vitro conditions.

Multi-objective shape optimization of double pipe heat exchanger with inner corrugated tube using RSM method

International Nuclear Information System (INIS)

Han, Huai-Zhi; Li, Bing-Xi; Wu, Hao; Shao, Wei

2015-01-01

Integrated a fully developing three-dimensional heat transfer and flow model, a multi-objective optimization aims to fulfill the geometric design for double-tube heat exchangers with inner corrugated tube is investigated in this work with RSM. Dimensionless corrugation pitch (p/D), dimensionless corrugation height (H/D), dimensionless corrugation radius (r/D) and Reynolds number (Re) are considered as four design parameters. Considering the process parameters, the characteristic numbers involving heat transfer characteristic, resistance characteristic and overall heat transfer performance calculated by CFD, and are served as objective functions to the RSM (Nu c , f c , Nu c /Nu s , f c /f s and h in this paper). The results of optimal designs are a set of multiple optimum solutions, called 'Pareto optimal solutions'. It reveals the identical tendency of Nu c /Nu s and f c /f s reflecting the conflict between them that means augmenting the heat transfer performance with various design parameters in the optimal situation inevitably sacrificed the increase of flow resistance. According to the Pareto optimal curves, the optimum designing parameters of double pipe heat exchanger with inner corrugated tube under the constrains of Nu c /Nu s ≥1.2 are found to be P/D = 0.82, H/D = 0.22, r/D = 0.23, Re = 26,263, corresponding to the maximum value of η = 1.12. (authors)

A PLIF and PIV study of liquid mixing enhanced by a lateral synthetic jet pair

International Nuclear Information System (INIS)

Xia Qingfeng; Zhong Shan

2012-01-01

Highlights: ► Enhancement of mixing between two water streams in a planar channel by means of a lateral synthetic jet pair is studied using PLIF and PIV. ► The excellent mixing observed is largely caused by a strong interaction between the opposing vortex pairs produced by the lateral synthetic jets. ► The synthetic jet operating conditions, at which a nearly homogenous mixing is achieved, are also identified and they are expressed in terms of a functional relationship. - Abstract: In this paper, enhancement of mixing between two water streams of the same flow rate in a planar channel by means of a lateral synthetic jet pair is studied at a net flow Reynolds number of 83 using PLIF and PIV. The synthetic jet pair is operated 180° out-of-phase at a range of actuation frequencies and displacements, with the latter being characterized by the dimensionless stroke length. The extent of mixing is evaluated using PLIF data at a location further downstream in the mixing channel. It is found that at a fixed actuation frequency a higher dimensionless stroke length produces a better mixing, and as the actuation frequency increases a lower dimensionless stroke length is required to achieve a given mixing degree. At a sufficiently high frequency or dimensionless stroke length, a nearly homogenous mixing with a mixing degree greater than 0.9 can be obtained. A functional relationship between actuation frequency and dimensionless stroke length is also obtained by best fitting the experimental data, which can be used for selecting the synthetic jet operating conditions to ensure a good mixing. Furthermore, both PLIF and PIV results show that each synthetic jet actuation cycle produce two opposing vortex pairs, which play an important role in prompting mixing between the two fluid streams. The excellent mixing obtained at a high frequency or a high dimensionless stroke length is found to be largely caused by a strong interaction between these opposing vortex pairs.

A note on the heat transfer in convective fins

International Nuclear Information System (INIS)

Razelos, P.

1979-01-01

In this paper a generalized approach to the problem of heat transfer through convective fins is given. The proper dimensionless variables, which specify the general problem are identified, and upper bounds of the values of the dimensionless number Nsub(r) defined as 'the ratio of the heat transferred by the fin to that of the corresponding bare surface' are derived. It was shown that these limiting values of the Nsub(r) are 1/√B 1 and √2/B 1 for longitudinal fins and spines respectively, where B 1 is the Biot number hb/k, while for annular fins of constant thickness and hyperbolic profile, Nsub(r) 1 , where K(β) is a number determined by the profile of the fin and the ratio β = x 2 /x 1 of the outside to the inside radii. It was also shown that for longitudinal fins and spinces the possible adverse insulating effect by the use of the fin is avoided, if one selects the value of √hA/kC [de

Surface wave propagation in an ideal Hall-magnetohydrodynamic plasma jet in flowing environment

International Nuclear Information System (INIS)

Sikka, Himanshu; Kumar, Nagendra; Zhelyazkov, Ivan

2004-01-01

The behavior of the Hall-magnetohydrodynamic (Hall-MHD) sausage and kink waves is studied in the presence of steady flow. The influence of the flow both inside and outside the plasma slab is taken into account. The plasma in the environment is considered to be cold and moves with the different flow velocity outside the slab. In the limit of parallel propagation, dispersion relation is derived to discuss the propagation of both the modes. Numerical results for the propagation characteristics are obtained for different Alfvenic Mach number ratios inside and outside the slab. It is found that the dispersion curves for both surface modes, namely, the sausage and kink ones in cold plasma show complexities in their behavior in terms of multivalued portions of the curves. These multivalued portions correspond to the different normalized phase velocities for the same value of Alfvenic Mach number. In contrast to the conventional MHD surface waves which are assumed to be pure surface waves or pseudosurface waves, surface waves are obtained which are bulk waves for very small dimensionless wave numbers, then turn to leaky waves and finally transform to pure surface waves for values of dimensionless wave number greater than one

Performance and optimum design of convective-radiative rectangular fin with convective base heating, wall conduction resistance, and contact resistance between the wall and the fin base

International Nuclear Information System (INIS)

Aziz, Abdul; Beers-Green, Arlen B.

2009-01-01

This paper investigates the performance and optimum design of a longitudinal rectangular fin attached to a convectively heated wall of finite thickness. The exposed surfaces of the fin lose heat to the environmental sink by simultaneous convection and radiation. The tip of the fin is assumed to lose heat by convection and radiation to the same sink. The analysis and optimization of the fin is conducted numerically using the symbolic algebra package Maple. The temperature distribution, the heat transfer rates, and the fin efficiency data is presented illustrating how the thermal performance of the fin is affected by the convection-conduction number, the radiation-conduction number, the base convection Biot number, the convection and radiation Biot numbers at the tip, and the dimensionless sink temperature. Charts are presented showing the relationship between the optimum convection-conduction number and the optimum radiation-conduction number for different values of the base convection Biot number and dimensionless sink temperature and fixed values of the convection and radiation Biot numbers at the tip. Unlike the few other papers which have applied the Adomian's decomposition and the differential quadrature element method to this problem but give illustrative results for specific fin geometry and thermal variables, the present graphical data are generally applicable and can be used by fin designers without delving into the mathematical details of the computational techniques.

Rotation induced flow suppression around two tandem circular cylinders at low Reynolds number

Energy Technology Data Exchange (ETDEWEB)

Chatterjee, Dipankar [Advanced Design and Analysis Group, CSIR—Central Mechanical Engineering Research Institute, Durgapur-713209 (India); Gupta, Krishan [Department of Mechanical Engineering, Sardar Vallabhai National Institute of Technology Surat, Surat-395007 (India); Kumar, Virendra [Department of Mechanical Engineering, Indian Institute of Technology Patna, Patna-800013 (India); Varghese, Sachin Abraham, E-mail: d_chatterjee@cmeri.res.in [Department of Mechanical Engineering, National Institute of Technology Durgapur, Durgapur-713209 (India)

2017-08-15

The rotation to a bluff object is known to have a stabilizing effect on the fluid dynamic transport around the body. An unsteady periodic flow can be degenerated into a steady flow pattern depending on the rate of rotation imparted to the body. On the other hand, multiple bodies placed in tandem arrangement with respect to an incoming flow can cause destabilization to the flow as a result of the complicated wake interaction between the bodies. Accordingly, the spacing between the bodies and the rate of rotation have significant impact on the overall fluid dynamic transport around them. The present work aims to understand how these two competing factors are actually influencing the fluidic transport across a pair of identical rotating circular cylinders kept in tandem arrangement in an unconfined medium. The cylinders are subjected to a uniform free stream flow and the gaps between the cylinders are varied as 0.2, 0.7, 1.5 and 3.0. Both the cylinders are made to rotate in the clockwise sense. The Reynolds number based on the free stream flow is taken as 100. A two-dimensional finite volume based transient computation is performed for a range of dimensionless rotational speeds of the cylinders (0 ≤ Ω ≤ 2.75). The results show that the shedding phenomena can be observed up to a critical rate of rotation (Ω{sub cr}) depending on the gap spacing. Beyond Ω{sub cr}, the flow becomes stabilized and finally completely steady as Ω increases further. Increasing the gap initially causes a slight decrease in the critical rotational speed, however, it increases at a rapid rate for larger gap spacing. (paper)

Number Sense on the Number Line

Science.gov (United States)

Woods, Dawn Marie; Ketterlin Geller, Leanne; Basaraba, Deni

2018-01-01

A strong foundation in early number concepts is critical for students' future success in mathematics. Research suggests that visual representations, like a number line, support students' development of number sense by helping them create a mental representation of the order and magnitude of numbers. In addition, explicitly sequencing instruction…

Stochastic field-line wandering in magnetic turbulence with shear. II. Decorrelation trajectory method

Science.gov (United States)

Negrea, M.; Petrisor, I.; Shalchi, A.

2017-11-01

We study the diffusion of magnetic field lines in turbulence with magnetic shear. In the first part of the series, we developed a quasi-linear theory for this type of scenario. In this article, we employ the so-called DeCorrelation Trajectory method in order to compute the diffusion coefficients of stochastic magnetic field lines. The magnetic field configuration used here contains fluctuating terms which are described by the dimensionless functions bi(X, Y, Z), i = (x, y) and they are assumed to be Gaussian processes and are perpendicular with respect to the main magnetic field B0. Furthermore, there is also a z-component of the magnetic field depending on radial coordinate x (representing the gradient of the magnetic field) and a poloidal average component. We calculate the diffusion coefficients for magnetic field lines for different values of the magnetic Kubo number K, the dimensionless inhomogeneous magnetic parallel and perpendicular Kubo numbers KB∥, KB⊥ , as well as Ka v=bya vKB∥/KB⊥ .

Impact of melting heat transfer and nonlinear radiative heat flux mechanisms for the generalized Burgers fluids

Directory of Open Access Journals (Sweden)

Waqar Azeem Khan

Full Text Available The present paper deals with the analysis of melting heat and mass transfer characteristics in the stagnation point flow of an incompressible generalized Burgers fluid over a stretching sheet in the presence of non-linear radiative heat flux. A uniform magnetic field is applied normal to the flow direction. The governing equations in dimensional form are reduced to a system of dimensionless expressions by implementation of suitable similarity transformations. The resulting dimensionless problem governing the generalized Burgers is solved analytically by using the homotopy analysis method (HAM. The effects of different flow parameters like the ratio parameter, magnetic parameter, Prandtl number, melting parameter, radiation parameter, temperature ratio parameter and Schmidt number on the velocity, heat and mass transfer characteristics are computed and presented graphically. Moreover, useful discussions in detail are carried out with the help of plotted graphs and tables. Keywords: Generalized Burgers fluid, Non-linear radiative flow, Magnetic field, Melting heat transfer

Damage in agitated vessels of large visco-elastic particles dispersed in a highly viscous fluid.

Science.gov (United States)

Bouvier, Laurent; Moreau, Anne; Line, Alain; Fatah, Nouria; Delaplace, Guillaume

2011-01-01

Many food recipes entail several homogenization steps for solid particles in hot or cold viscous liquids, such as pureed fruit and sugar, jam or sauce with mushroom pieces. Unfortunately, these unavoidable processes induce damage to the solid particles. To date, little is known of the extent and nature of the damage caused. Consequently, few clear guidelines are available for monitoring solid particle integrity when mixing solid/liquid suspensions in an agitated tank. In this study, an attempt is made to quantify the impact of various physical parameters including the influence of the rotational speed of the impeller and the processing time on particle attrition, when a suspension of large visco-elastic particles in a highly viscous fluid is mixed under isothermal condition. Pectin gel particles were immerged in a viscous liquid and homogenized for various times and rotational speeds, while the evolution of the particle's morphological parameters was monitored. Then, a set of dimensionless numbers governing the attrition mechanism is established and some empirical process relationships are proposed to correlate these numbers to the morphological characteristics and mass balance ratios. From the conditions observed, it is clear that 2 dimensionless ratios could be responsible for a change in the damaging mechanisms. These 2 ratios are the Froude and impeller rotation numbers. Finally, in the conditions tested, mass balance ratios appear to be mainly sensitive to the impeller rotational number, while the shape ratios are both impacted by the Froude and impeller rotational numbers. Damage to solid particles suspended in a stirred vessel reduce the final product quality in industrial cooking processes. Examples of this are fruit in jam or sauces with mushroom pieces. The attrition phenomenon was measured and the influences of the impeller rotational speed and processing time were evaluated quantitatively in function of dimensionless numbers. This study contributes key

Effect of thermal radiation and Hall current on heat and mass transfer of unsteady MHD flow of a viscoelastic micropolar fluid through a porous medium

Directory of Open Access Journals (Sweden)

B.I. Olajuwon

2014-12-01

Full Text Available Heat and mass transfer effects on unsteady flow of a viscoelastic micropolar fluid over an infinite moving permeable plate in a saturated porous medium in the presence of a transverse magnetic field with Hall effect and thermal radiation are studied. The governing system of partial differential equations is transformed to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using perturbation technique to obtain the expressions for velocity, microrotation, temperature and concentration. With the help of graphs, the effects of magnetic field parameter M, thermal radiation parameter Nr, Hall current parameter m, K, viscoelastic parameter a, and slip parameter h on the velocity, microrotation, temperature and concentration fields within the boundary layer are discussed. The result showed that increase in Nr and m increases translational velocity across the boundary layer while (a decreases translational velocity in the vicinity of the plate but the reverse happens when away from the plate. As h increases the translational velocity across the boundary layer increases. The higher the values of Nr, the higher the micro-rotational velocity effect while m lowers it. Also the effects n, a, m, Nr, Pr and Sc on the skin friction coefficient, Nusselt number and Sherwood numbers are presented numerically in tabular form. The result also revealed that increase in n reduces the skin friction coefficient. Pr enhances the rate of heat transfer while Sc enhances the rate of mass transfer.

Number names and number understanding

DEFF Research Database (Denmark)

Ejersbo, Lisser Rye; Misfeldt, Morten

2014-01-01

This paper concerns the results from the first year of a three-year research project involving the relationship between Danish number names and their corresponding digits in the canonical base 10 system. The project aims to develop a system to help the students’ understanding of the base 10 syste...... the Danish number names are more complicated than in other languages. Keywords: A research project in grade 0 and 1th in a Danish school, Base-10 system, two-digit number names, semiotic, cognitive perspectives....

Numerical investigation of potential stratification caused by a cryogenic helium spill inside a tunnel

Science.gov (United States)

Sinclair, Cameron; Malecha, Ziemowit; Jedrusyna, Artur

2018-04-01

The sudden release of cryogenic fluid into an accelerator tunnel can pose a significant health and safety risk. For this reason, it is important to evaluate the consequences of such a spill. Previous publications concentrated on either Oxygen Deficiency Hazard or the evaluation of mathematical models using experimental data. No studies to date have focussed on the influence of cryogen inlet conditions on flow development. In this paper, the stratification behaviour of low-temperature helium released into an air-filled accelerator tunnel is investigated for varying helium inlet diameters. A numerical model was constructed using the OpenFOAM Toolbox of a generalised 3D geometry, with similar hydraulic characteristics to the CERN and SLAC tunnels. This model has been validated against published experimental and numerical data. A dimensionless parameter, based on Bakke number, was then determined for the onset of stratification, taking into account the helium inlet diameter; a dimensionless parameter for the degree of stratification was also employed. The simulated flow behaviour is described in terms of these dimensionless parameters, as well as the temperature and oxygen concentration at various heights throughout the tunnel.

Thermal efficiency maximization for H- and X-shaped heat exchangers based on constructal theory

International Nuclear Information System (INIS)

Chen, Lingen; Feng, Huijun; Xie, Zhihui; Sun, Fengrui

2015-01-01

Constructal optimizations of H- and X-shaped heat exchangers are carried out by taking the maximum thermal efficiency (the ratio of the dimensionless heat transfer rate to the dimensionless total pumping power) as optimization objective. The constraints of total tube volumes and spaces occupied by heat exchangers are considered in the optimizations. For the H-shaped heat exchanger, the thermal efficiency decreases when the dimensionless mass flow rate increases. For the higher order of the X-shaped heat exchanger, when the order number is 3, the thermal efficiency of the heat exchanger with Murry law is increased by 68.54% than that with equal flow velocity in the tubes, and by 435.46% than that with equal cross section area of the tubes. - Highlights: • Constructal optimizations of H- and X-shaped heat exchangers are carried out. • Maximum thermal efficiency is taken as optimization objective. • Thermal efficiency is defined as ratio of heat transfer rate to total pumping power. • Optimal constructs of H- and X-shaped heat exchangers are obtained. • Thermal efficiency of X-shaped heat exchanger is larger than that of H-shaped.

The IEC-publication 336/1981 - new formulation of the standards for X-ray foci

International Nuclear Information System (INIS)

Geldner, E.; Schnitger, H.

1982-01-01

With the new IEC-standard for foci a clear distinction has been made between application oriented focus classification, expressed by the focus nominal value as a dimensionless number and the detectable real geometric focus measured in the sense of the principle 'Truth in advertising'. Now, even regions of a size [de

The Radio And Very Low Frequency (VLF) Electromagnetic ...

African Journals Online (AJOL)

The Radio And Very Low Frequency (VLF) Electromagnetic Response Of A Layered Earth Media With Variable Dielectric Permittivity. ... A radio frequency of 125 KHz and a very low frequency (VLF) of 20 KHz were used in the computations and the field parameters studied over a dimensionless induction number, B. The ...

Dimensional Analysis

Indian Academy of Sciences (India)

Dimensional analysis is a useful tool which finds important applications in physics and engineering. It is most effective when there exist a maximal number of dimensionless quantities constructed out of the relevant physical variables. Though a complete theory of dimen- sional analysis was developed way back in 1914 in a.

EFFECT OF DISCRETE HEATER AT THE VERTICAL WALL OF THE CAVITY OVER THE HEAT TRANSFER AND ENTROPY GENERATION USING LBM

Directory of Open Access Journals (Sweden)

Mousa Farhadi

2011-01-01

Full Text Available In this paper Lattice Boltzmann Method (LBM was employed for investigation the effect of the heater location on flow pattern, heat transfer and entropy generation in a cavity. A 2D thermal lattice Boltzmann model with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations were performed for Rayleigh numbers from 103 to 106 at Pr = 0.71. The study was carried out for heater length of 0.4 side wall length which is located at the right side wall. Results are presented in the form of streamlines, temperature contours, Nusselt number and entropy generation curves. Results show that the location of heater has a great effect on the flow pattern and temperature fields in the enclosure and subsequently on entropy generation. The dimensionless entropy generation decreases at high Rayleigh number for all heater positions. The ratio of averaged Nusselt number and dimensionless entropy generation for heater located on vertical and horizontal walls was calculated. Results show that higher heat transfer was observed from the cold walls when the heater located on vertical wall. On the other hand, heat transfer increases from the heater surface when it located on the horizontal wall.

Weighting factor for instantaneous source functions of a permeable ...

African Journals Online (AJOL)

A multiplicative weighting factor, E, is obtained which shows constant behaviour at late dimensionless flow times for a particular set of well and reservoir dimensionless parameters. Computation of dimensionless pressures using the factor shows conformity with expected behaviour for a layered reservoir with crossflow ...

Disentangling the origins of torque enhancement through wall roughness in Taylor-Couette turbulence

NARCIS (Netherlands)

Zhu, Xiaojue; Verzicco, Roberto; Lohse, Detlef

2017-01-01

Direct numerical simulations (DNS) are performed to analyse the global transport properties of turbulent Taylor-Couette flow with inner rough wall up to Taylor number Ta = 1010. The dimensionless torque Nuω shows an effective scaling of Nuω ∝ Ta0.42±0.01, which is steeper than the ultimate regime

Sum rules, asymptotic behaviour and (multi)baryon states in the Skyrme model

International Nuclear Information System (INIS)

Mignaco, J.A.; Wulck, S.

1990-01-01

We obtain sum roles that should be satisfied by the solutions of the Euler-Lagrange equation for the chiral angle in the Skyrme model in the hedgehog representation. The sum rules allow to determine the existence of solutions with integer baryon number for well determined values of a relevant dimensionless parameter Φ only. For all other values, there are no solutions with integer baryon number, in particular for the pure non-linear sigma model. (author)

Energetics of the multi-phase fluid flow in a narrow kerf in laser cutting conditions

Science.gov (United States)

Golyshev, A. A.; Orishich, A. M.; Shulyatyev, V. B.

2016-10-01

The energy balance of the multi-phase medium flow is studied experimentally under the laser cutting. Experimental data are generalized due to the condition of minimal roughness of the created surface used as a quality criterion of the melt flow, and also due to the application of dimensionless parameters: Peclet number and dimensionless absorbed laser power. For the first time ever it is found that, regardless the assistant gas (oxygen or nitrogen), laser type (the fiber one with the wavelength of 1.07 µm or CO2-laser with the wavelength of 10.6 µm), the minimal roughness is provided at a certain energy input in a melt unit, about 26 J/mm3. With oxygen, 50% of this input is provided by the radiation, the other 50% - by the exothermic reaction of iron oxidation.

Vibration of heat exchange components in liquid and two-phase cross-flow

International Nuclear Information System (INIS)

Pettigrew, M.J.

1978-05-01

Heat exchange components must be analysed at the design stage to avoid flow-induced vibration problems. This paper presents information required to formulate flow-induced vibration excitation mechanisms in liquid and two-phase cross-flow. Three basic excitation mechanisms are considered, namely: 1) fluidelastic instability, 2) periodic wake shedding, and 3) response to random flow turbulence. The vibration excitation information is deduced from vibration response data for various types of tube bundles. Sources of information are: 1) fundamental studies on tube bundles, 2) model testing, 3) field measurements, and 4) operating experiences. Fluidelastic instability is formulated in terms of dimensionless flow velocity and dimensionless damping; periodic wake shedding in terms of Strouhal number and lift coefficient; and random turbulence excitation in terms of statistical parameters of random forces. Guidelines are recommended for design purposes. (author)

EFFECT OF HYDRAULIC AND GEOMETRICAL PROPERTIES ON STEPPED CASCADE AERATION SYSTEM

Directory of Open Access Journals (Sweden)

VEDHACHALAM RATHINAKUMAR

2017-03-01

Full Text Available Stepped cascade aeration system is commonly used to aerate the water and wastewater to increase the dissolved oxygen during pre and post treatment process. In the present research, experiments were conducted to evaluate the performance of a rectangular Cascade Aeration System with varying flow rates, risers and tread by maintaining constant width of the channel using water collected from reverse osmosis plant. The experiments were carried out with four different risers such as 0.15 m, 0.18 m, 0.225 m and 0.30 m. Each rise was investigated with five different tread of 0.60 m, 0.55 m, 0.50 m, 0.45 m and 0.40 m. Comprehensive experimental investigations were carried out for different hydraulic loading rates of 0.005 to 0.035 m3/s/m2. Results obtained from the experiments reveals that increasing dimensionless discharges promotes more aeration, attains a maximum up to dimensionless discharge= 2.22 and beyond this there was a significant decrease in aeration. In addition, the increased in number of steps significantly enhances air entertainment and surface fall rate in the Stepped Cascade Aeration System. A regression equation was derived by keeping aeration efficiency as response with dimensionless discharge and oxygen saturation concentration as influencing parameters. The dimension less discharge is a function of critical depth of the rectangular channel and step height, whereas oxygen saturation concentration represents the ratio of oxygen deficit and oxygen saturation concentration. Based on the experimental results, the optimum design and/or results such as number of steps (12 numbers and hydraulic loading rate (0.025 m3/s/m2 with fixed tread width of 0.6 m were identified to achieve maximum aeration rate (0.5-0.60 in Aeration system.

PECULIARITIES OF GENERALIZATION OF SIMILAR PHENOMENA IN THE PROCESS OF FISH HEAT TREATMENT

Directory of Open Access Journals (Sweden)

V. A. Pokhol’chenko

2015-01-01

Full Text Available The theoretical presuppositions for the possibility of generalizing and similarity founding in dehydration and wet materials heating processes are studieded in this article. It is offered to carry out the given processes generalization by using dimensionless numbers of similarity. At the detailed analyzing of regularities of heat treatment processes of fish in different modes a significant amount of experienced material was successfully generalized on the basis of dimensionless simplex (similarity numbers. Using the dimensionless simplex allowed to detect a number of simple mathematical models for the studied phenomena. The generalized kinetic models of fish dehydration, the generalized dynamic models (changing moisture diffusion coefficients, the generalized kinetic models of fish heating (the temperature field changing in the products thickness, average volume and center were founded. These generalized mathematical models showed also relationship of dehydration and heating at the processes of fish semi-hot, hot smoking (drying and frying. The relationship of the results from the physical nature of the dehydration process, including a change in the binding energy of the moisture with the material to the extent of the process and the shrinkage impact on the rate of the product moisture removal is given in the article. The factors influencing the internal structure and properties of the raw material changing and retarding the dehydration processes are described there. There was a heating rate dependence of fish products on the chemical composition the geometric dimensions of the object of heating and on the coolant regime parameters. A unique opportunity is opened by using the generalized models, combined with empirically derived equations and the technique of engineering calculation of these processes, to design a rational modes of heat treatment of raw materials and to optimize the performance of thermal equipment.

Magnetic field line random walk in two-dimensional dynamical turbulence

Science.gov (United States)

Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.

2017-08-01

The field line random walk (FLRW) of magnetic turbulence is one of the important topics in plasma physics and astrophysics. In this article, by using the field line tracing method, the mean square displacement (MSD) of FLRW is calculated on all possible length scales for pure two-dimensional turbulence with the damping dynamical model. We demonstrate that in order to describe FLRW with the damping dynamical model, a new dimensionless quantity R is needed to be introduced. On different length scales, dimensionless MSD shows different relationships with the dimensionless quantity R. Although the temporal effect affects the MSD of FLRW and even changes regimes of FLRW, it does not affect the relationship between the dimensionless MSD and dimensionless quantity R on all possible length scales.

Cosmic numbers the numbers that define our universe

CERN Document Server

Stein, James D

2011-01-01

Our fascination with numbers begins when we are children and continues throughout our lives. We start counting our fingers and toes and end up balancing checkbooks and calculating risk. So powerful is the appeal of numbers that many people ascribe to them a mystical significance. Other numbers go beyond the supernatural, working to explain our universe and how it behaves. In Cosmic Numbers , mathematics professor James D. Stein traces the discovery, evolution, and interrelationships of the numbers that define our world. Everyone knows about the speed of light and absolute zero, but numbers lik

[Intel random number generator-based true random number generator].

Science.gov (United States)

Huang, Feng; Shen, Hong

2004-09-01

To establish a true random number generator on the basis of certain Intel chips. The random numbers were acquired by programming using Microsoft Visual C++ 6.0 via register reading from the random number generator (RNG) unit of an Intel 815 chipset-based computer with Intel Security Driver (ISD). We tested the generator with 500 random numbers in NIST FIPS 140-1 and X(2) R-Squared test, and the result showed that the random number it generated satisfied the demand of independence and uniform distribution. We also compared the random numbers generated by Intel RNG-based true random number generator and those from the random number table statistically, by using the same amount of 7500 random numbers in the same value domain, which showed that the SD, SE and CV of Intel RNG-based random number generator were less than those of the random number table. The result of u test of two CVs revealed no significant difference between the two methods. Intel RNG-based random number generator can produce high-quality random numbers with good independence and uniform distribution, and solves some problems with random number table in acquisition of the random numbers.

Hydrodynamic structure of the boundary layers in a rotating cylindrical cavity with radial inflow

International Nuclear Information System (INIS)

Herrmann-Priesnitz, Benjamín; Torres, Diego A.; Calderón-Muñoz, Williams R.; Salas, Eduardo A.; Vargas-Uscategui, Alejandro; Duarte-Mermoud, Manuel A.

2016-01-01

A flow model is formulated to investigate the hydrodynamic structure of the boundary layers of incompressible fluid in a rotating cylindrical cavity with steady radial inflow. The model considers mass and momentum transfer coupled between boundary layers and an inviscid core region. Dimensionless equations of motion are solved using integral methods and a space-marching technique. As the fluid moves radially inward, entraining boundary layers develop which can either meet or become non-entraining. Pressure and wall shear stress distributions, as well as velocity profiles predicted by the model, are compared to numerical simulations using the software OpenFOAM. Hydrodynamic structure of the boundary layers is governed by a Reynolds number, Re, a Rossby number, Ro, and the dimensionless radial velocity component at the periphery of the cavity, U_o. Results show that boundary layers merge for Re > 0.1, and boundary layers become predominantly non-entraining for low Ro, low Re, and high U_o. Results may contribute to improve the design of technology, such as heat exchange devices, and turbomachinery.

Relaxation of an unsteady turbulent boundary layer on a flat plate in an expansion tube

Science.gov (United States)

Gurta, R. N.; Trimpi, R. L.

1974-01-01

An analysis is presented for the relaxation of a turbulent boundary layer on a semi-infinite flat plate after passage of a shock wave and a trailing driver gas-driven gas interface. The problem has special application to expansion-tube flows. The flow-governing equations have been transformed into the Crocco variables, and a time-similar solution is presented in terms of the dimensionless distance-time variable alpha and the dimensionless velocity variable beta. An eddy-viscosity model, similar to that of time-steady boundary layers, is applied to the inner and outer regions of the boundary layer. A turbulent Prandtl number equal to the molecular Prandtl number is used to relate the turbulent heat flux to the eddy viscosity. The numerical results, obtained by using the Gauss-Seidel line-relaxation method, indicate that a fully turbulent boundary layer relaxes faster to the final steady-state values of heat transfer and skin friction than a laminar boundary layer. The results also give a fairly good estimate of the local skin friction and heat transfer for near steady-flow conditions.

Hydrodynamic structure of the boundary layers in a rotating cylindrical cavity with radial inflow

Energy Technology Data Exchange (ETDEWEB)

Herrmann-Priesnitz, Benjamín, E-mail: bherrman@ing.uchile.cl; Torres, Diego A. [Department of Mechanical Engineering, Universidad de Chile, Beauchef 851, Santiago (Chile); Advanced Mining Technology Center, Universidad de Chile, Av. Tupper 2007, Santiago (Chile); Calderón-Muñoz, Williams R. [Department of Mechanical Engineering, Universidad de Chile, Beauchef 851, Santiago (Chile); Energy Center, Universidad de Chile, Av. Tupper 2007, Santiago (Chile); Salas, Eduardo A. [CSIRO-Chile International Centre of Excellence, Apoquindo 2827, Floor 12, Santiago (Chile); Vargas-Uscategui, Alejandro [Department of Mechanical Engineering, Universidad de Chile, Beauchef 851, Santiago (Chile); CSIRO-Chile International Centre of Excellence, Apoquindo 2827, Floor 12, Santiago (Chile); Duarte-Mermoud, Manuel A. [Advanced Mining Technology Center, Universidad de Chile, Av. Tupper 2007, Santiago (Chile); Department of Electrical Engineering, Universidad de Chile, Av. Tupper 2007, Santiago (Chile)

2016-03-15

A flow model is formulated to investigate the hydrodynamic structure of the boundary layers of incompressible fluid in a rotating cylindrical cavity with steady radial inflow. The model considers mass and momentum transfer coupled between boundary layers and an inviscid core region. Dimensionless equations of motion are solved using integral methods and a space-marching technique. As the fluid moves radially inward, entraining boundary layers develop which can either meet or become non-entraining. Pressure and wall shear stress distributions, as well as velocity profiles predicted by the model, are compared to numerical simulations using the software OpenFOAM. Hydrodynamic structure of the boundary layers is governed by a Reynolds number, Re, a Rossby number, Ro, and the dimensionless radial velocity component at the periphery of the cavity, U{sub o}. Results show that boundary layers merge for Re < < 10 and Ro > > 0.1, and boundary layers become predominantly non-entraining for low Ro, low Re, and high U{sub o}. Results may contribute to improve the design of technology, such as heat exchange devices, and turbomachinery.

Axial velocity profiles and secondary flows of developing laminar flows in a straight connected exit region of a 180 .deg. square curved duct

Energy Technology Data Exchange (ETDEWEB)

Sohn, Hyun Chull; Lee, Heang Nam; Park, Gil Moon [Chosun Univ., Gwangju (Korea, Republic of)

2005-10-01

In the present study, characteristics of steady state laminar flows of a straight duct connected to a 180 .deg. curved duct were examined in the entrance region through experimental and numerical analyses. For the analysis, the governing equations of laminar flows in the Cartesian coordinate system were applied. Flow characteristics such as velocity profiles and secondary flows were investigated numerically and experimentally in a square cross-sectional straight duct by the PIV system and a CFD code (STARCD). For the PIV measurement, smoke particles produced from mosquito coils. The experimental data were obtained at 9 points dividing the test sections by 400 mm. Experimental and numerical results can be summarized as follows. 1) Reynolds number, Re was increased, dimensionless velocity profiles at the outer wall were increased due to the effect of the centrifugal force and secondary flows. 2) The intensity of a secondary flow became stronger at the inner wall rather than the outer wall regardless of Reynolds number. Especially, fluid dynamic phenomenon called conner impact were observed at dimensionless axial position, x/D{sub h}=50.

The Mental Number Line in Dyscalculia: Impaired Number Sense or Access from Symbolic Numbers?

Science.gov (United States)

Lafay, Anne; St-Pierre, Marie-Catherine; Macoir, Joël

2017-01-01

Numbers may be manipulated and represented mentally over a compressible number line oriented from left to right. According to numerous studies, one of the primary reasons for dyscalculia is related to improper understanding of the mental number line. Children with dyscalculia usually show difficulty when they have to place Arabic numbers on a…

Froude number fractions to increase walking pattern dynamic similarities: application to plantar pressure study in healthy subjects.

Science.gov (United States)

Moretto, P; Bisiaux, M; Lafortune, M A

2007-01-01

The purpose of this study was to determine if using similar walking velocities obtained from fractions of the Froude number (N(Fr)) and leg length can lead to kinematic and kinetic similarities and lower variability. Fifteen male subjects walked on a treadmill at 0.83 (VS(1)) and 1.16ms(-1) (VS(2)) and then at two similar velocities (V(Sim27) and V(Sim37)) determined from two fractions of the N(Fr) (0.27 and 0.37) so that the average group velocity remained unchanged in both conditions (VS(1)=V (Sim27)andVS(2)=V (Sim37)). N(Fr) can theoretically be used to determine walking velocities proportional to leg lengths and to establish dynamic similarities between subjects. This study represents the first attempt at using this approach to examine plantar pressure. The ankle and knee joint angles were studied in the sagittal plane and the plantar pressure distribution was assessed with an in-shoe measurement device. The similarity ratios were computed from anthropometric parameters and plantar pressure peaks. Dynamically similar conditions caused a 25% reduction in leg joint angles variation and a 10% significant decrease in dimensionless pressure peak variability on average of five footprint locations. It also lead to heel and under-midfoot pressure peaks proportional to body mass and to an increase in the number of under-forefoot plantar pressure peaks proportional to body mass and/or leg length. The use of walking velocities derived from N(Fr) allows kinematic and plantar pressure similarities between subjects to be observed and leads to a lower inter-subject variability. In-shoe pressure measurements have proven to be valuable for the understanding of lower extremity function. Set walking velocities used for clinical assessment mask the effects of body size and individual gait mechanics. The anthropometric scaling of walking velocities (fraction of N(Fr)) should improve identification of unique walking strategies and pathological foot functions.

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African Journals Online (AJOL)

De Don

where ;_ is the Frank-Kamenetski i parameter. 0 is the dimensionless temperature variable, (5 is the dimensionless combustible variable and r is the dimensionless radial distance variable. For different values of nand m, we have the following cases subject to the boundary conditions. For Slab: Case 1; n = 0, m = -2 ...

Dimensional analysis of flame angles versus wind speed

Science.gov (United States)

Robert E. Martin; Mark A. Finney; Domingo M. Molina; David B. Sapsis; Scott L. Stephens; Joe H. Scott; David R. Weise

1991-01-01

Dimensional analysis has potential to help explain and predict physical phenomena, but has been used very little in studies of wildland fire behavior. By combining variables into dimensionless groups, the number of variables to be handled and the experiments to be run is greatly reduced. A low velocity wind tunnel was constructed, and methyl, ethyl, and isopropyl...

THE RELATIONSHIP BETWEEN NUMBER NAMES AND NUMBER CONCEPTS

DEFF Research Database (Denmark)

Ejersbo, Lisser Rye; Misfeldt, Morten

Different countries have different names for numbers. These names are often related in a regular way to the base-10 place value system used for writing numbers as digits. However, in several languages, this regularity breaks down (e.g., between 10 and 20), and there is limited knowledge of how th......, a second, regular set of number names is introduced in primary school. The study’s findings suggest that the regularity of number names influences the development of number concepts and creates a positive impact on the understanding of the base-10 system....

A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler Numbers

Directory of Open Access Journals (Sweden)

J. Y. Kang

2013-01-01

Full Text Available Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomials Ũn(x. We observe an interesting phenomenon of “scattering” of the zeros of the polynomials Ũn(x in complex plane. We find out some identities and properties related to polynomials Ũn(x. Finally, we also derive interesting relations between polynomials Ũn(x, Stirling numbers, central factorial numbers, and Euler numbers.

Some investigations on the mean and fluctuating velocities of an oscillating Taylor bubble

International Nuclear Information System (INIS)

Madani, Sara; Caballina, Ophelie; Souhar, Mohamed

2012-01-01

Highlights: ► The unsteady motion of an oscillating Taylor bubble has been studied. ► A non-dimensionalized velocity differential equation is numerically solved. ► The role of dimensionless numbers on the dynamics of the bubble is highlighted. ► Mean and fluctuating velocities and the phase shift are experimentally investigated. ► Correlations allowing the prediction of these latter parameters are proposed. - Abstract: The slug flow characterized by large elongated bubbles also called Taylor bubbles is widely encountered in nuclear reactor steam generators, cooling plants, reboilers, etc. The analysis of slug flow is very important as the instability caused by such flows can affect the safety features of nuclear reactors and other two-phase flow equipments. In this paper, we study the motion of a Taylor bubble rising in stagnant fluids in a vertical oscillating pipe. The investigation is restricted to high Reynolds numbers and to an intermediate range of Bond numbers where the effects of surface tension can be considered. The Froude number ranged between 0.22 and 0.33. Firstly, detailed analysis of models proposed in the literature for the motion of a Taylor bubble in an unsteady acceleration field is realized. The velocity differential equation obtained in the case of potential and axisymmetric flow without surface tension given in the literature is first non-dimensionalized to highlight dimensionless numbers. Then, the instantaneous velocity of the bubble is numerically determined. Mean and fluctuating velocities as well as the phase shift (U ¯ b , U f and φ) are estimated by using a technique based on the nonlinear least squares method. Results enable a discussion on the role played by dimensionless numbers on the dynamics of the bubble. It is found that the two parameters, the relative acceleration and the Bond number (a and Bo) have a governing role on the evolution of mean and fluctuating velocities while the ratio of the oscillation amplitude to

The effect of fluid flow due to the crystal-melt density change on the growth of a parabolic isothermal dendrite

Science.gov (United States)

Mcfadden, G. B.; Coriell, S. R.

1986-01-01

The Ivantsov (1947) analysis of an isolated isothermal dendrite (with zero surface tension) growing into a supercooled liquid is extended to include the effects of the fluid flow due to volume contraction or expansion upon solidification. For an axisymmetric paraboloidal dendrite, an analytic solution to the Navier-Stokes equations is obtained. The magnitude of the flow is proportional to the relative density change epsilon, and the flow becomes negligible far from the surface of the dendrite. The temperature field consistent with this flow can also be found explicitly. The well-known expression that relates the dimensionless supercooling to the Peclet number in the absence of fluid flow is modified for nonzero epsilon, but the effect is of order epsilon and hence is seen to be minor for most values of epsilon and dimensionless supercooling that occur in practice.

Straight flavor of Binary Number in Decimal Number System

OpenAIRE

MD. Abdul Awal Ansary; Sushanta Acharjee

2012-01-01

Different number systems are available on the basis of their base numbers. For instance, decimal number system is of base 10, hexadecimal number system which base is 16 and, Binary number system which base is 2 etc. Some numbers systems are easy to understand by the human being and some are easy to understand by electronics machine for instance digital computers. Computers only can understand data and instructions that are stored in binary form, though we input the data and instruction in dec...

An autostratigraphic view of the long-term dynamics of delta distributary channels: A new step forward with the grade index model

Science.gov (United States)

Naruse, H.; Muto, T.

2017-12-01

Autostratigraphy is the stratigraphy that is generated by large-scale, deterministic autogenic processes of depositional systems, based on the full recognition of non-equilibrium behavior in response to steady external forcing. Recent experimental studies to explore the effects of basin water depth on the dynamics of distributary channels have brought a new geometrical scheme, here referred to as the grade index model, which is expected to make a significant step forward for development of the autostratigraphy of river deltas. Grade index (0 ≤ Gindex ≤1) is a dimensionless number that describes how close the alluvial river is to a graded state and is given as the ratio of subaerial allocation of the supplied sediment to both subaerial and subaqueous allocation of the sediment, in the form of a function of dimensionless basin water depth (h*). The grade index model for a particular geometrical setting suggests that as h* increase toward +∞, all of dimensionless magnitudes of delta progradation rate (Rpro*), alluvial aggradation rate (Ragg*), channel migration rate (Rmig*), avulsion frequency decrease toward 0, and all of dimensionless timescales of channel shifting (τs*), recurrence of channels (τr*), channel avulsion (τA*) increase toward +∞, and also that Rpro* = Ragg* = Rmig* = fA* = (τs*)-1 = (τr*)-1 = (τA* )-1 = Gindex. This grade index model, despite its simple structure, offers deep insight into the rationale of shoreline autoretreat, a typical large-scale, deterministic autogenic process that is realized by non-equilibrium response to steady base level rise. A simple geometrical modeling leads to a finding that Ppro* = (1 - Ab*) Gindex, where Ab* is a dimensionless form of the bottom surface of the deltaic deposit (Ab) given by dividing Ab with the square of autostratigraphic length scale (Λ). As the delta grows with base level rise, Ab progressively increases and then inevitably meets an event that Ab* exceeds 1 (i.e. Ab exceeds Λ2). We also

Transition Heat Transfer Modeling Based on the Characteristics of Turbulent Spots

Science.gov (United States)

Simon, Fred; Boyle, Robert

1998-01-01

While turbulence models are being developed which show promise for simulating the transition region on a turbine blade or vane, it is believed that the best approach with the greatest potential for practical use is the use of models which incorporate the physics of turbulent spots present in the transition region. This type of modeling results in the prediction of transition region intermittency which when incorporated in turbulence models give a good to excellent prediction of the transition region heat transfer. Some models are presented which show how turbulent spot characteristics and behavior can be employed to predict the effect of pressure gradient and Mach number on the transition region. The models predict the spot formation rate which is needed, in addition to the transition onset location, in the Narasimha concentrated breakdown intermittency equation. A simplified approach is taken for modeling turbulent spot growth and interaction in the transition region which utilizes the turbulent spot variables governing transition length and spot generation rate. The models are expressed in terms of spot spreading angle, dimensionless spot velocity, dimensionless spot area, disturbance frequency and Mach number. The models are used in conjunction with a computer code to predict the effects of pressure gradient and Mach number on the transition region and compared with VKI experimental turbine data.

Effect of Using Extra Fins on the Pin Fin Classic Geometry for Enhancement Heat Sink Performance using EGM Method

Directory of Open Access Journals (Sweden)

Kadhum Audaa Jehhef

2018-04-01

Full Text Available In the present study, the effect of new cross-section fin geometries on overall thermal/fluid performance had been investigated. The cross-section included the base original geometry of (triangular, square, circular, and elliptical pin fins by adding exterior extra fins along the sides of the origin fins. The present extra fins include rectangular extra fin of 2 mm (height and 4 mm (width and triangular extra fin of 2 mm (base 4 mm (height. The use of entropy generation minimization method (EGM allows the combined effect of thermal resistance and pressure drop to be assessed through the simultaneous interaction with the heat sink. A general dimensionless expression for the entropy generation rate is obtained by considering a control volume around the pin fin including a base plate and applying the conservations equations of mass and energy with the entropy balance. The dimensionless numbers used includes the aspect ratio (ε, Reynolds number (Re, Nusselt number (Nu, and the drag coefficients (CD. Fourteen different cross-section fin geometries are examined for the heat transfer, fluid friction, and the minimum entropy generation rate. The results showed that the Nusselt number increases with increasing the Reynolds number for all employed models. The ellipse models (ET and ER-models give the highest value in the Nusselt number as compared with the classical pin fins. The fin of the square geometry with four rectangular extra fins (SR-models gives an agreement in Nusselt number as compared with the previous study.

Sagan numbers

OpenAIRE

Mendonça, J. Ricardo G.

2012-01-01

We define a new class of numbers based on the first occurrence of certain patterns of zeros and ones in the expansion of irracional numbers in a given basis and call them Sagan numbers, since they were first mentioned, in a special case, by the North-american astronomer Carl E. Sagan in his science-fiction novel "Contact." Sagan numbers hold connections with a wealth of mathematical ideas. We describe some properties of the newly defined numbers and indicate directions for further amusement.

STUDY OF POND WATER QUALITY BY THE ASSESSMENT OF PHYSICOCHEMICAL PARAMETERS AND WATER QUALITY INDEX

OpenAIRE

Vinod Jena; Satish Dixit; Ravi ShrivastavaSapana Gupta; Sapana Gupta

2013-01-01

Water quality index (WQI) is a dimensionless number that combines multiple water quality factors into a single number by normalizing values to subjective rating curves. Conventionally it has been used for evaluating the quality of water for water resources suchas rivers, streams and lakes, etc. The present work is aimed at assessing the Water Quality Index (W.Q.I) ofpond water and the impact of human activities on it. Physicochemical parameters were monitored for the calculation of W.Q.I for ...

Sedimentological regimes for turbidity currents: Depth-averaged theory

Science.gov (United States)

Halsey, Thomas C.; Kumar, Amit; Perillo, Mauricio M.

2017-07-01

Turbidity currents are one of the most significant means by which sediment is moved from the continents into the deep ocean; their properties are interesting both as elements of the global sediment cycle and due to their role in contributing to the formation of deep water oil and gas reservoirs. One of the simplest models of the dynamics of turbidity current flow was introduced three decades ago, and is based on depth-averaging of the fluid mechanical equations governing the turbulent gravity-driven flow of relatively dilute turbidity currents. We examine the sedimentological regimes of a simplified version of this model, focusing on the role of the Richardson number Ri [dimensionless inertia] and Rouse number Ro [dimensionless sedimentation velocity] in determining whether a current is net depositional or net erosional. We find that for large Rouse numbers, the currents are strongly net depositional due to the disappearance of local equilibria between erosion and deposition. At lower Rouse numbers, the Richardson number also plays a role in determining the degree of erosion versus deposition. The currents become more erosive at lower values of the product Ro × Ri, due to the effect of clear water entrainment. At higher values of this product, the turbulence becomes insufficient to maintain the sediment in suspension, as first pointed out by Knapp and Bagnold. We speculate on the potential for two-layer solutions in this insufficiently turbulent regime, which would comprise substantial bedload flow with an overlying turbidity current.

Transfer coefficients in elliptical tubes and plate fin heat exchangers

International Nuclear Information System (INIS)

Saboya, S.M.

1979-09-01

Mean transfer coefficients in elliptical tubes and plate fin heat exchangers were determined by application of heat and mass transfer analogy in conjunction with the naphthalene sublimation technique. The transfer coefficients are presented in a dimensionless form as functions of the Reynolds number. By using the least squares method analytical expressions for the transfer coefficients were determined with low scattering. (E.G.) [pt

Bernoulli-Carlitz and Cauchy-Carlitz numbers with Stirling-Carlitz numbers

OpenAIRE

Kaneko, Hajime; Komatsu, Takao

2017-01-01

Recently, the Cauchy-Carlitz number was defined as the counterpart of the Bernoulli-Carlitz number. Both numbers can be expressed explicitly in terms of so-called Stirling-Carlitz numbers. In this paper, we study the second analogue of Stirling-Carlitz numbers and give some general formulae, including Bernoulli and Cauchy numbers in formal power series with complex coefficients, and Bernoulli-Carlitz and Cauchy-Carlitz numbers in function fields. We also give some applications of Hasse-Teichm...

Photon number projection using non-number-resolving detectors

International Nuclear Information System (INIS)

Rohde, Peter P; Webb, James G; Huntington, Elanor H; Ralph, Timothy C

2007-01-01

Number-resolving photo-detection is necessary for many quantum optics experiments, especially in the application of entangled state preparation. Several schemes have been proposed for approximating number-resolving photo-detection using non-number-resolving detectors. Such techniques include multi-port detection and time-division multiplexing. We provide a detailed analysis and comparison of different number-resolving detection schemes, with a view to creating a useful reference for experimentalists. We show that the ideal architecture for projective measurements is a function of the detector's dark count and efficiency parameters. We also describe a process for selecting an appropriate topology given actual experimental component parameters

Multiple Long-Time Solutions for Intermediate Reynolds Number Flow past a Circular Cylinder with a Nonlinear Inertial and Dissipative Attachment

Science.gov (United States)

Blanchard, Antoine B. E.; Bergman, Lawrence A.; Vakakis, Alexander F.; Pearlstein, Arne J.

2016-11-01

We consider two-dimensional flow past a linearly-sprung cylinder allowed to undergo rectilinear motion normal to the mean flow, with an attached "nonlinear energy sink" consisting of a mass allowed to rotate about the cylinder axis, and whose rotational motion is linearly damped by a viscous damper. For Re fluid density, dimensionless damping coefficient, and ratio of the rotating mass to the total mass, we find that different inlet transients lead to different long-time solutions, including solutions that are steady and symmetric (with a motionless cylinder), time-periodic, quasi-periodic, and chaotic. The results show that over a wide range of the parameters, the steady symmetric motionless-cylinder solution is locally, but not globally, stable. Supported by NSF Grant CMMI-1363231.

On the Role of Dimensionless Elastic Fracture Mechanics.

Science.gov (United States)

1985-07-03

34.’ . . . .- . . - . . . - ... - . .. . . . . . -8-.V 6. B.M. Wundt , "A Unified Interpretation of Room Temperature Strength of Notched...207s (1948). D.H. Winne and B.M. Wundt , Application of the Griffith-Irwin theory of crack propagation to the bursting behavior of disks, including... Wundt , A unified interpretation of room-temperature strength of notched specimens as influenced by their size. Metals Engng. Conf., ASME Paper No

Dimensionless energy confinement scaling in W7-AS

International Nuclear Information System (INIS)

Preuss, R.; Dose, V.

2001-01-01

Energy confinement in W7-AS has been analyzed in terms of dimensionally exact form free functions employing Bayesian probability theory. The confinement function was set up as a linear combination of dimensionally exact power law terms as already proposed very early by Connor and Taylor. Generation of this expansion basis is dictated by the basic plasma model which one assumes. Based upon data accumulated in W7-AS, which contains the energy content for a wide variety of variable settings, predictions for single variable scans are made. The scaling functions for density and power scans, respectively, are in quantitative agreement with data collected in W7-AS. The result of a single variable scan is therefore already hidden in the data obtained for arbitrary variable choices and can be extracted from the latter by a proper data analysis. Furthermore, the optimal model for the description of the global transport in W7-AS is identified as the collisional low beta kinetic model. (author)

Dimensionless energy confinement scaling in W7-AS

International Nuclear Information System (INIS)

Preuss, R.; Dose, V.; Linden, W. von der

1999-01-01

Energy confinement in W7-AS has been analyzed in terms of dimensionally exact form free functions employing Bayesian probability theory. The confinement function was set up as a linear combination of dimensionally exact power law terms as already proposed very early by Connor and Taylor. Generation of this expansion basis is dictated by the basic plasma model which one assumes. Based upon data accumulated in W7-AS, which contains the energy content for a wide variety of variable settings, predictions for single variable scans are made. The scaling functions for density and power scans, respectively, are in quantitative agreement with data collected in W7-AS. The result of a single variable scan is therefore already hidden in the data obtained for arbitrary variable choices and can be extracted from the latter by a proper data analysis. Furthermore, the optimal model for the description of the global transport in W7-AS is identified as the collisional low beta kinetic model. (author)

Parametric study on single shot peening by dimensional analysis method incorporated with finite element method

Science.gov (United States)

Wu, Xian-Qian; Wang, Xi; Wei, Yan-Peng; Song, Hong-Wei; Huang, Chen-Guang

2012-06-01

Shot peening is a widely used surface treatment method by generating compressive residual stress near the surface of metallic materials to increase fatigue life and resistance to corrosion fatigue, cracking, etc. Compressive residual stress and dent profile are important factors to evaluate the effectiveness of shot peening process. In this paper, the influence of dimensionless parameters on maximum compressive residual stress and maximum depth of the dent were investigated. Firstly, dimensionless relations of processing parameters that affect the maximum compressive residual stress and the maximum depth of the dent were deduced by dimensional analysis method. Secondly, the influence of each dimensionless parameter on dimensionless variables was investigated by the finite element method. Furthermore, related empirical formulas were given for each dimensionless parameter based on the simulation results. Finally, comparison was made and good agreement was found between the simulation results and the empirical formula, which shows that a useful approach is provided in this paper for analyzing the influence of each individual parameter.

Radiated chemical reaction impacts on natural convective MHD mass transfer flow induced by a vertical cone

Science.gov (United States)

Sambath, P.; Pullepu, Bapuji; Hussain, T.; Ali Shehzad, Sabir

2018-03-01

The consequence of thermal radiation in laminar natural convective hydromagnetic flow of viscous incompressible fluid past a vertical cone with mass transfer under the influence of chemical reaction with heat source/sink is presented here. The surface of the cone is focused to a variable wall temperature (VWT) and wall concentration (VWC). The fluid considered here is a gray absorbing and emitting, but non-scattering medium. The boundary layer dimensionless equations governing the flow are solved by an implicit finite-difference scheme of Crank-Nicolson which has speedy convergence and stable. This method converts the dimensionless equations into a system of tri-diagonal equations and which are then solved by using well known Thomas algorithm. Numerical solutions are obtained for momentum, temperature, concentration, local and average shear stress, heat and mass transfer rates for various values of parameters Pr, Sc, λ, Δ, Rd are established with graphical representations. We observed that the liquid velocity decreased for higher values of Prandtl and Schmidt numbers. The temperature is boost up for decreasing values of Schimdt and Prandtl numbers. The enhancement in radiative parameter gives more heat to liquid due to which temperature is enhanced significantly.

Pore to core scale simulation of the mass transfer with mineral reaction in porous media

International Nuclear Information System (INIS)

Bekri, S.; Renard, S.; Delprat-Jannaud, F.

2015-01-01

Pore Network Model (PNM) is used to simulate mass transfer with mineral reaction in a single phase flow through porous medium which is here a sandstone sample from the reservoir formation of the Pakoslaw gas field. The void space of the porous medium is represented by an idealized geometry of pore-bodies joined by pore-throats. Parameters defining the pore-bodies and the pore-throats distribution are determined by an optimization process aiming to match the experimental Mercury Intrusion Capillary Pressure (MICP) curve and petrophysical properties of the rock such as intrinsic permeability and formation factor. The generated network is used first to simulate the multiphase flow by solving Kirchhoff's laws. The capillary pressure and relative permeability curves are derived. Then, reactive transport is addressed under asymptotic regime where the solute concentration undergoes an exponential evolution with time. The porosity/ permeability relationship and the three phenomenological coefficients of transport, namely the solute velocity, the dispersion and the mean reaction rate are determined as functions of Peclet and Peclet-Damkohler dimensionless numbers. Finally, the role of the dimensionless numbers on the reactive flow properties is highlighted. (authors)

Thermo-economic multi-objective optimization of solar dish-Stirling engine by implementing evolutionary algorithm

International Nuclear Information System (INIS)

Ahmadi, Mohammad H.; Sayyaadi, Hoseyn; Mohammadi, Amir H.; Barranco-Jimenez, Marco A.

2013-01-01

Highlights: • Thermo-economic multi-objective optimization of solar dish-Stirling engine is studied. • Application of the evolutionary algorithm is investigated. • Error analysis is done to find out the error through investigation. - Abstract: In the recent years, remarkable attention is drawn to Stirling engine due to noticeable advantages, for instance a lot of resources such as biomass, fossil fuels and solar energy can be applied as heat source. Great number of studies are conducted on Stirling engine and finite time thermo-economic is one of them. In the present study, the dimensionless thermo-economic objective function, thermal efficiency and dimensionless power output are optimized for a dish-Stirling system using finite time thermo-economic analysis and NSGA-II algorithm. Optimized answers are chosen from the results using three decision-making methods. Error analysis is done to find out the error through investigation

Numerical study of unsteady MHD oblique stagnation point flow and heat transfer due to an oscillating stream

Science.gov (United States)

Javed, T.; Ghaffari, A.; Ahmad, H.

2016-05-01

The unsteady stagnation point flow impinging obliquely on a flat plate in presence of a uniform applied magnetic field due to an oscillating stream has been studied. The governing partial differential equations are transformed into dimensionless form and the stream function is expressed in terms of Hiemenz and tangential components. The dimensionless partial differential equations are solved numerically by using well-known implicit finite difference scheme named as Keller-box method. The obtained results are compared with those available in the literature. It is observed that the results are in excellent agreement with the previous studies. The effects of pertinent parameters involved in the problem namely magnetic parameter, Prandtl number and impinging angle on flow and heat transfer characteristics are illustrated through graphs. It is observed that the influence of magnetic field strength increases the fluid velocity and by the increase of obliqueness parameter, the skin friction increases.

Scattering of atoms by solid surfaces: A CCGM theory of diffraction by a one-dimensional stationary periodic wall

International Nuclear Information System (INIS)

Goodman, F.O.; Scribani, L.

1981-01-01

The CCGM theory of elastic atom--surface scattering, proposed by Cabrera, Celli, Goodman, and Manson [Surf. Sci. 19, 67 (1970)], is applied to the now-popular corrugated wall model of the scattering. Instead of the original ''hard'' wall, a ''softer'' wall, with finite potential step height, is used. The CCGM soft-wall results are compared with corresponding exact hard-wall results, for corrugations of the sinusoidal type and of other types, for example those with nondifferentiable corrugation functions. It is concluded that the CCGM soft-wall results agree well with the exact hard-wall results provided that neither the dimensionless corrugation amplitude nor the dimensionless atom wave number is too large, although no explanation of the reason for this agreement is given. The results are important because a typical exact calculation may be far more time consuming than is a typical CCGM calculation, particularly for the ''nastier'' corrugation functions

Nice numbers

CERN Document Server

Barnes, John

2016-01-01

In this intriguing book, John Barnes takes us on a journey through aspects of numbers much as he took us on a geometrical journey in Gems of Geometry. Similarly originating from a series of lectures for adult students at Reading and Oxford University, this book touches a variety of amusing and fascinating topics regarding numbers and their uses both ancient and modern. The author intrigues and challenges his audience with both fundamental number topics such as prime numbers and cryptography, and themes of daily needs and pleasures such as counting one's assets, keeping track of time, and enjoying music. Puzzles and exercises at the end of each lecture offer additional inspiration, and numerous illustrations accompany the reader. Furthermore, a number of appendices provides in-depth insights into diverse topics such as Pascal’s triangle, the Rubik cube, Mersenne’s curious keyboards, and many others. A theme running through is the thought of what is our favourite number. Written in an engaging and witty sty...

Eulerian numbers

CERN Document Server

Petersen, T Kyle

2015-01-01

This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group. The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions. The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, ...

Floating Breakwaters: State-of-the-Art Literature Review.

Science.gov (United States)

1981-10-01

estructure draft (feet) Do 0 structure offset distance for offset breakwater (feet) ) t diameter of scrap tire (feet) 16 SYMBOLS AND DEFINITIONS...mooring line effeL. on roll (degrees) m effective porosity ot poro,,s breakwater (dimensionless) estructure mass (pu::,rJs per second squared per foot...dimensionless) NAf Nyquist frequency (one per second) P load or surface pressure (pounds) estructure porosity (dimensionless) PD dissipated wave power (foot

Diamond Fuzzy Number

Directory of Open Access Journals (Sweden)

T. Pathinathan

2015-01-01

Full Text Available In this paper we define diamond fuzzy number with the help of triangular fuzzy number. We include basic arithmetic operations like addition, subtraction of diamond fuzzy numbers with examples. We define diamond fuzzy matrix with some matrix properties. We have defined Nested diamond fuzzy number and Linked diamond fuzzy number. We have further classified Right Linked Diamond Fuzzy number and Left Linked Diamond Fuzzy number. Finally we have verified the arithmetic operations for the above mentioned types of Diamond Fuzzy Numbers.

Proth Numbers

Directory of Open Access Journals (Sweden)

Schwarzweller Christoph

2015-02-01

Full Text Available In this article we introduce Proth numbers and prove two theorems on such numbers being prime [3]. We also give revised versions of Pocklington’s theorem and of the Legendre symbol. Finally, we prove Pepin’s theorem and that the fifth Fermat number is not prime.

Rational-number comparison across notation: Fractions, decimals, and whole numbers.

Science.gov (United States)

Hurst, Michelle; Cordes, Sara

2016-02-01

Although fractions, decimals, and whole numbers can be used to represent the same rational-number values, it is unclear whether adults conceive of these rational-number magnitudes as lying along the same ordered mental continuum. In the current study, we investigated whether adults' processing of rational-number magnitudes in fraction, decimal, and whole-number notation show systematic ratio-dependent responding characteristic of an integrated mental continuum. Both reaction time (RT) and eye-tracking data from a number-magnitude comparison task revealed ratio-dependent performance when adults compared the relative magnitudes of rational numbers, both within the same notation (e.g., fractions vs. fractions) and across different notations (e.g., fractions vs. decimals), pointing to an integrated mental continuum for rational numbers across notation types. In addition, eye-tracking analyses provided evidence of an implicit whole-number bias when we compared values in fraction notation, and individual differences in this whole-number bias were related to the individual's performance on a fraction arithmetic task. Implications of our results for both cognitive development research and math education are discussed. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Those fascinating numbers

CERN Document Server

Koninck, Jean-Marie De

2009-01-01

Who would have thought that listing the positive integers along with their most remarkable properties could end up being such an engaging and stimulating adventure? The author uses this approach to explore elementary and advanced topics in classical number theory. A large variety of numbers are contemplated: Fermat numbers, Mersenne primes, powerful numbers, sublime numbers, Wieferich primes, insolite numbers, Sastry numbers, voracious numbers, to name only a few. The author also presents short proofs of miscellaneous results and constantly challenges the reader with a variety of old and new n

Triangular Numbers

Indian Academy of Sciences (India)

Admin

Triangular number, figurate num- ber, rangoli, Brahmagupta–Pell equation, Jacobi triple product identity. Figure 1. The first four triangular numbers. Left: Anuradha S Garge completed her PhD from. Pune University in 2008 under the supervision of Prof. S A Katre. Her research interests include K-theory and number theory.

Correlation for prediction of growing and detaching bubble contact diameter on a heating wall

International Nuclear Information System (INIS)

Chen Deqi; Pan Liangming; Huang Yanping

2011-01-01

Phenomenal and theoretical analysis on the evolution of bubble contact diameter during bubble growing is presented in this paper, and it was found that the bubble contact diameter is dependent on the bubble growth rate and bubble radius strongly. By analyzing the regarding experimental data published in the literature, the relation between dimensionless bubble contact diameter, and dimensionless bubble growth time is obtained, based on this relation, a correlation relative to dimensionless bubble growth rate and dimensionless bubble radius are proposed for prediction of bubble contact diameter. With proper values of coefficients, a w and n w , this correlation can well predict the bubble contact diameter data published in the literature, with an error within ±20%. (authors)

Comparative study of chemo-electro-mechanical transport models for an electrically stimulated hydrogel

International Nuclear Information System (INIS)

Elshaer, S E; Moussa, W A

2014-01-01

The main objective of this work is to introduce a new expression for the hydrogel’s hydration for use within the Poisson Nernst–Planck chemo electro mechanical (PNP CEM) transport models. This new contribution to the models support large deformation by considering the higher order terms in the Green–Lagrangian strain tensor. A detailed discussion of the CEM transport models using Poisson Nernst–Planck (PNP) and Poisson logarithmic Nernst–Planck (PLNP) equations for chemically and electrically stimulated hydrogels will be presented. The assumptions made to simplify both CEM transport models for electric field application in the order of 0.833 kV m −1 and a highly diluted electrolyte solution (97% is water) will be explained. This PNP CEM model has been verified accurately against experimental and numerical results. In addition, different definitions for normalizing the parameters are used to derive the dimensionless forms of both the PNP and PLNP CEM. Four models, PNP CEM, PLNP CEM, dimensionless PNP CEM and dimensionless PNLP CEM transport models were employed on an axially symmetric cylindrical hydrogel problem with an aspect ratio (diameter to thickness) of 175:3. The displacement and osmotic pressure obtained for the four models are compared against the variation of the number of elements for finite element analysis, simulation duration and solution rate when using the direct numerical solver. (papers)

Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers

International Nuclear Information System (INIS)

Ônishi, Yoshihiro

2011-01-01

The three fundamental properties of the Bernoulli numbers, namely, the von Staudt-Clausen theorem, von Staudt's second theorem, and Kummer's original congruence, are generalized to new numbers that we call generalized Bernoulli-Hurwitz numbers. These are coefficients in the power series expansion of a higher-genus algebraic function with respect to a suitable variable. Our generalization differs strongly from previous works. Indeed, the order of the power of the modulus prime in our Kummer-type congruences is exactly the same as in the trigonometric function case (namely, Kummer's own congruence for the original Bernoulli numbers), and as in the elliptic function case (namely, H. Lang's extension for the Hurwitz numbers). However, in other past results on higher-genus algebraic functions, the modulus was at most half of its value in these classical cases. This contrast is clarified by investigating the analogue of the three properties above for the universal Bernoulli numbers. Bibliography: 34 titles.

Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers

Energy Technology Data Exchange (ETDEWEB)

Onishi, Yoshihiro [Faculty of Education Human Sciences, University of Yamanashi, Takeda, Kofu (Japan)

2011-10-31

The three fundamental properties of the Bernoulli numbers, namely, the von Staudt-Clausen theorem, von Staudt's second theorem, and Kummer's original congruence, are generalized to new numbers that we call generalized Bernoulli-Hurwitz numbers. These are coefficients in the power series expansion of a higher-genus algebraic function with respect to a suitable variable. Our generalization differs strongly from previous works. Indeed, the order of the power of the modulus prime in our Kummer-type congruences is exactly the same as in the trigonometric function case (namely, Kummer's own congruence for the original Bernoulli numbers), and as in the elliptic function case (namely, H. Lang's extension for the Hurwitz numbers). However, in other past results on higher-genus algebraic functions, the modulus was at most half of its value in these classical cases. This contrast is clarified by investigating the analogue of the three properties above for the universal Bernoulli numbers. Bibliography: 34 titles.

Flow friction and heat transfer of ethanol–water solutions through silicon microchannels

International Nuclear Information System (INIS)

Wu Huiying; Wu Xinyu; Wei Zhen

2009-01-01

An experimental investigation was performed on the flow friction and convective heat transfer characteristics of the ethanol–water solutions flowing through five sets of trapezoidal silicon microchannels having hydraulic diameters ranging from 141.7 µm to 268.6 µm. Four kinds of ethanol–water solutions with the ethanol volume concentrations ranging from 0 to 0.8 were tested under different flow and heating conditions. It was found that the cross-sectional geometric parameters had great effect on the flow friction and heat transfer, and the microchannels with a larger W b /W t (bottom width-to-top width ratio) and a smaller H/W t (depth-to-top width ratio) usually had a larger friction constant and a higher Nusselt number. Entrance effects were significant for the flow friction and heat transfer in silicon microchannels, and decreased with the increase of dimensionless hydrodynamic length L and dimensionless thermal length L + h . When L > 1.0, the hydrodynamic entrance effect on the flow friction was ignorable. For the developed laminar flow in silicon microchannels, the Navier–Stokes equation was applicable. It was also found that the volume concentrations had different effects on the flow friction and heat transfer. Within the experimental range, the effect of volume concentrations on the flow friction was ignorable, and the friction constants of the ethanol–water solutions having different concentrations were the same as those of the pure water. However, volume concentrations had great effect on the convection heat transfer in silicon microchannels. With the increase of the volume concentrations, the Nusselt number of the ethanol–water solutions increased obviously, which was attributed to the combination effect of the increase in the Prantdtl number as well as the volatilization effect of the ethanol. Based on the experimental data, the dimensionless correlations for the flow friction and heat transfer of the ethanol–water solutions in the silicon

A Resolution of the Paradox of Enrichment

Science.gov (United States)

Feng, Z. C.; Li, Y. Charles

2015-06-01

The paradox of enrichment was observed by Rosenzweig [1971] in a class of predator-prey models. Two of the parameters in the models are crucial for the paradox. These two parameters are the prey's carrying capacity and prey's half-saturation for predation. Intuitively, increasing the carrying capacity due to enrichment of the prey's environment should lead to a more stable predator-prey system. Analytically, it turns out that increasing the carrying capacity always leads to an unstable predator-prey system that is susceptible to extinction from environmental random perturbations. This is the so-called paradox of enrichment. Our resolution here rests upon a closer investigation on a dimensionless number H formed from the carrying capacity and the prey's half-saturation. By recasting the models into dimensionless forms, the models are in fact governed by a few dimensionless numbers including H. The effects of the two parameters: carrying capacity and half-saturation are incorporated into the number H. In fact, increasing the carrying capacity is equivalent (i.e. has the same effect on H) to decreasing the half-saturation which implies more aggressive predation. Since there is no paradox between more aggressive predation and instability of the predator-prey system, the paradox of enrichment is resolved. The so-called instability of the predator-prey system is characterized by the existence of a stable limit cycle in the phase plane, which gets closer and closer to the predator axis and prey axis. Due to random environmental perturbations, this can lead to extinction. We also further explore spatially dependent models for which the phase space is infinite-dimensional. The spatially independent limit cycle which is generated by a Hopf bifurcation from an unstable steady state, is linearly stable in the infinite-dimensional phase space. Numerical simulations indicate that the basin of attraction of the limit cycle is riddled. This shows that spatial perturbations can

Hupa Numbers.

Science.gov (United States)

Bennett, Ruth, Ed.; And Others

An introduction to the Hupa number system is provided in this workbook, one in a series of numerous materials developed to promote the use of the Hupa language. The book is written in English with Hupa terms used only for the names of numbers. The opening pages present the numbers from 1-10, giving the numeral, the Hupa word, the English word, and…

Direct-contact condensation regime map for core makeup tank of passive reactors

International Nuclear Information System (INIS)

Lee, Sang Il; No, Hee Cheon

1998-01-01

The condensation regime map in the core makeup tank of passive reactors is experimentally investigated. The condensation regimes identified through the experiments are divided into three distinct ones: sonic jet, subsonic jet, and steam cavity. The steam cavity regime is a unique regime of downward injection with the present geometry not previously observed in other experiments. The condensation regime map is constructed using Froude number and Jacob number. It turns out that the buoyancy force has a large influence on the regime transition because the regime map using the Froude number better fits data with different geometries than other dimensionless parameters. Simple correlations for the regime boundaries are proposed using the Froude number and the Jacob number

HEAT AND MASS TRANSFER EFFECTS ON FLOW PAST PARABOLIC STARTING MOTION OF ISOTHERMAL VERTICAL PLATE IN THE PRESENCE OF FIRST ORDER CHEMICAL REACTION

Directory of Open Access Journals (Sweden)

R. Muthucumaraswamy

2013-06-01

Full Text Available An exact solution of unsteady flow past a parabolic starting motion of the infinite isothermal vertical plate with uniform mass diffusion, in the presence of a homogeneous chemical reaction of the first order, has been studied. The plate temperature and the concentration level near the plate are raised uniformly. The dimensionless governing equations are solved using the Laplace transform technique. The effect of velocity profiles are studied for different physical parameters, such as chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number, and time. It is observed that velocity increases with increasing values of thermal Grashof number or mass Grashof number. The trend is reversed with respect to the chemical reaction parameter.

Thermodynamic optimization of a coiled tube heat exchanger under constant wall heat flux condition

International Nuclear Information System (INIS)

Satapathy, Ashok K.

2009-01-01

In this paper the second law analysis of thermodynamic irreversibilities in a coiled tube heat exchanger has been carried out for both laminar and turbulent flow conditions. The expression for the scaled non-dimensional entropy generation rate for such a system is derived in terms of four dimensionless parameters: Prandtl number, heat exchanger duty parameter, Dean number and coil to tube diameter ratio. It has been observed that for a particular value of Prandtl number, Dean number and duty parameter, there exists an optimum diameter ratio where the entropy generation rate is minimum. It is also found that with increase in Dean number or Reynolds number, the optimum value of the diameter ratio decreases for a particular value of Prandtl number and heat exchanger duty parameter.

Approximation of complex algebraic numbers by algebraic numbers of bounded degree

OpenAIRE

Bugeaud, Yann; Evertse, Jan-Hendrik

2007-01-01

We investigate how well complex algebraic numbers can be approximated by algebraic numbers of degree at most n. We also investigate how well complex algebraic numbers can be approximated by algebraic integers of degree at most n+1. It follows from our investigations that for every positive integer n there are complex algebraic numbers of degree larger than n that are better approximable by algebraic numbers of degree at most n than almost all complex numbers. As it turns out, these numbers ar...

Temperature and heat flux scaling laws for isoviscous, infinite Prandtl number mixed heating convection.

Science.gov (United States)

Vilella, Kenny; Deschamps, Frederic

2018-04-01

Thermal evolution of terrestrial planets is controlled by heat transfer through their silicate mantles. A suitable framework for modelling this heat transport is a system including bottom heating (from the core) and internal heating, e.g., generated by secular cooling or by the decay of radioactive isotopes. The mechanism of heat transfer depends on the physical properties of the system. In systems where convection is able to operate, two different regimes are possible depending on the relative amount of bottom and internal heating. For moderate internal heating rates, the system is composed of active hot upwellings and cold downwellings. For large internal heating rates, the bottom heat flux becomes negative and the system is only composed of active cold downwellings. Here, we build theoretical scaling laws for both convective regimes following the approach of Vilella & Kaminski (2017), which links the surface heat flux and the temperature jump across both the top and bottom thermal boundary layer (TBL) to the Rayleigh number and the dimensionless internal heating rate. Theoretical predictions are then verified against numerical simulations performed in 2D and 3D-Cartesian geometry, and covering a large range of the parameter space. Our theoretical scaling laws are more successful in predicting the thermal structure of systems with large internal heating rates than that of systems with no or moderate internal heating. The differences between moderate and large internal heating rates are interpreted as differences in the mechanisms generating thermal instabilities. We identified three mechanisms: conductive growth of the TBL, instability impacting, and TBL erosion, the last two being present only for moderate internal heating rates, in which hot plumes are generated at the bottom of the system and are able to reach the surface. Finally, we apply our scaling laws to the evolution of the early Earth, proposing a new model for the cooling of the primordial magma ocean

Analytical and numerical stability analysis of Soret-driven convection in a horizontal porous layer: the effect of conducting bounding plates

Energy Technology Data Exchange (ETDEWEB)

Ouattara, B; Khouzam, A; Mojtabi, A [Universite de Toulouse (France); INPT, UPS (France); IMFT (Institut de Mecanique des Fluides de Toulouse), Allee Camille Soula, F-31400 Toulouse (France); Charrier-Mojtabi, M C, E-mail: bouattar@imft.fr, E-mail: akhouzam@imft.fr, E-mail: mojtabi@imft.fr, E-mail: cmojtabi@cict.fr [PHASE, EA 810, UFR PCA, Universite Paul Sabatier, 118 route de Narbonne, 31062 Toulouse cedex (France)

2012-06-01

The aim of this study was to investigate the effect of conducting boundaries on the onset of convection in a binary fluid-saturated porous layer. The isotropic saturated porous layer is bounded by two impermeable but thermally conducting plates, subjected to a constant heat flux. These plates have identical conductivity. Moreover, the conductivity of the plates is generally different from the porous layer conductivity. The overall layer is of large extent in both horizontal directions. The problem is governed by seven dimensionless parameters, namely the normalized porosity of the medium {epsilon}, the ratio of plates over the porous layer thickness {delta} and their relative thermal conductivities ratio d, the separation ratio {delta}, the Lewis number Le and thermal Rayleigh number Ra. In this work, an analytical and numerical stability analysis is performed. The equilibrium solution is found to lose its stability via a stationary bifurcation or a Hopf bifurcation depending on the values of the dimensionless parameters. For the long-wavelength mode, the critical Rayleigh number is obtained as Ra{sub cs}=12(1+2d{delta} )/[1+{psi} (2d{delta}Le+Le+1)] and k{sub cs}=0 for {psi}> {psi} {sub uni}> 0. This work extends an earlier paper by Mojtabi and Rees (2011 Int. J. Heat Mass Transfer 54 293-301) who considered a configuration where the porous layer is saturated by a pure fluid.

Beurling generalized numbers

CERN Document Server

Diamond, Harold G; Cheung, Man Ping

2016-01-01

"Generalized numbers" is a multiplicative structure introduced by A. Beurling to study how independent prime number theory is from the additivity of the natural numbers. The results and techniques of this theory apply to other systems having the character of prime numbers and integers; for example, it is used in the study of the prime number theorem (PNT) for ideals of algebraic number fields. Using both analytic and elementary methods, this book presents many old and new theorems, including several of the authors' results, and many examples of extremal behavior of g-number systems. Also, the authors give detailed accounts of the L^2 PNT theorem of J. P. Kahane and of the example created with H. L. Montgomery, showing that additive structure is needed for proving the Riemann hypothesis. Other interesting topics discussed are propositions "equivalent" to the PNT, the role of multiplicative convolution and Chebyshev's prime number formula for g-numbers, and how Beurling theory provides an interpretation of the ...

One-dimensional model of steady, compressible channel flow with mass, momentum, and energy addition

International Nuclear Information System (INIS)

Johnston, S.C.

1976-09-01

A one-dimensional model of steady, compressible channel flow with mass, momentum and energy addition is discussed. An exact solution to the governing equations was found and from it a similarity parameter relating dimensionless mass, momentum and energy addition identified. This similarity parameter is used to make two flows having different dimensionless mass, momentum and energy additions equivalent. Application of the similarity parameter to the LASL Intense Neutron Source experiment and the Sandia simulation of that experiment results in an expression relating the dimensionless mass addition of combustible gas required in the Sandia experiment to dimensionless energy addition in the LASL experiment. Results of the analysis indicate that the Sandia experiment can realistically simulate the energy addition in the LASL Intense Neutron Source experiment

Parcperdue Geopressure--Geothermal Project: Appendix B

Energy Technology Data Exchange (ETDEWEB)

Sweezy, L.R.

1981-10-05

The reservoir models used to perform the drawdown and buildup pressure analyses consist of analytic forms in lieu of the finite difference or numeric simulator types. Analytic models are derived from solutions of the diffusion equation which relate a pressure response with time and distance in the reservoir for a specified flow system. Solutions of the diffusion equation are obtained through mathematical methods such as Laplace transforms, Fourier transforms, Neuman's product techniques and Green's functions. Before an analytic solution is derived, the diffusivity equation is expressed in terms of dimensionless potential (m{sub D}), dimensionless distance (r{sub D}) and dimensionless time (t{sub D}). For the cylindrical coordinate case, the diffusivity equation in dimensionless form for a geopressured system is given.

Parametric Study on the Characteristics of Multiphase Laminar Flow with Density Difference in Various Microchannels

International Nuclear Information System (INIS)

Paek, Seung Ho; Kim, Dong Sung; Choi, Young Ki

2009-01-01

In this paper, we have performed a parametric study on the characteristics of multiphase laminar flow with density difference in various microchannels. The interface between multiphase fluids is rotated by the gravitational forces induced by density difference. The numerical simulations were carried out via commercial CFD package to study the characteristics of multiphase laminar flow. The results of the numerical simulations in this study were verified by comparing with the previously reported experimental results in the literature. We have also proposed a new dimensionless relationship between dimensionless rotation angle of interface and dimensionless parameters are proposed for square microchannels with various aspect ratios. The dimensionless relationship could be widely applied to the reliable design of various microfluidic devices dealing with multiphase laminar flow

Angular circulation speed of tablets in a vibratory tablet coating pan.

Science.gov (United States)

Kumar, Rahul; Wassgren, Carl

2013-03-01

In this work, a single tablet model and a discrete element method (DEM) computer simulation are developed to obtain the angular circulation speed of tablets in a vibratory tablet coating pan for range of vibration frequencies and amplitudes. The models identify three important dimensionless parameters that influence the speed of the tablets: the dimensionless amplitude ratio (a/R), the Froude number (aω2/g), and the tablet-wall friction coefficient, where a is the peak vibration amplitude at the drum center, ω is the vibration angular frequency, R is the drum radius, and g is the acceleration due to gravity. The models predict that the angular circulation speed of tablets increases with an increase in each of these parameters. The rate of increase in the angular circulation speed is observed to decrease for larger values of a/R. The angular circulation speed reaches an asymptote beyond a tablet-wall friction coefficient value of about 0.4. Furthermore, it is found that the Froude number should be greater than one for the tablets to start circulating. The angular circulation speed increases as Froude number increases but then does not change significantly at larger values of the Froude number. Period doubling, where the motion of the bed is repeated every two cycles, occurs at a Froude number larger than five. The single tablet model, although much simpler than the DEM model, is able to predict the maximum circulation speed (the limiting case for a large value of tablet-wall friction coefficient) as well as the transition to period doubling.

p-adic numbers

OpenAIRE

Grešak, Rozalija

2015-01-01

The field of real numbers is usually constructed using Dedekind cuts. In these thesis we focus on the construction of the field of real numbers using metric completion of rational numbers using Cauchy sequences. In a similar manner we construct the field of p-adic numbers, describe some of their basic and topological properties. We follow by a construction of complex p-adic numbers and we compare them with the ordinary complex numbers. We conclude the thesis by giving a motivation for the int...

Unsteady natural convection flow past an accelerated vertical plate in a thermally stratified fluid

Directory of Open Access Journals (Sweden)

Deka Rudra Kt.

2009-01-01

Full Text Available An exact solution to one-dimensional unsteady natural convection flow past an infinite vertical accelerated plate, immersed in a viscous thermally stratified fluid is investigated. Pressure work term and the vertical temperature advection are considered in the thermodynamic energy equation. The dimensionless governing equations are solved by Laplace Transform techniques for the Prandtl number unity. The velocity and temperature profiles as well as the skin-friction and the rate of heat transfer are presented graphically and discussed the effects of the Grashof number Gr, stratification parameter S at various times t.

Structuring polymer blends with bicontinuous phase morphology. Part II. Tailoring blends with ultralow critical volume fraction

DEFF Research Database (Denmark)

Lyngaae-Jørgensen, Jørgen; Utracki, Leszek

2003-01-01

A hypothesis providing a guideline for the development of immiscible polymer blends with co-continuous phase structure at very low critical volume fraction of one component is. postulated and experimentally verified. Based on a number of simplifying assumptions the following relation was derived......: phi(cr) = k(lambdagamma)(1-z)/(theta(b)(*))(z) where lambdagamma is a Deborah number and theta(b)(*) is a dimensionless break-up time. The equation parameters, k and z are constant that depend on the flow field hence on the blending equipment. For the studies an internal mixer with Walzenkneter...

An alternative form of the Darcy equation

Directory of Open Access Journals (Sweden)

Awad Mohamed M.

2014-01-01

Full Text Available This study presents an alternative form of the Darcy equation. This alternative form will be presented with the use of Bejan number (Be in the Left Hand Side (LHS of the equation. The main advantage in this alternative form of the Darcy equation is presenting both the Left Hand Side (LHS and the Right Hand Side (RHS as dimensionless quantities. For instance, this is similar to the relation of Fanning friction factor with Reynolds number for Hagen-Poiseuille flow (fully developed laminar flow in a circular pipe.

Effects of rotation on MHD flow past an accelerated isothermal vertical plate with heat and mass diffusion

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2010-01-01

Full Text Available An exact analysis of rotation effects on unsteady flow of an incompressible and electrically conducting fluid past a uniformly accelerated infinite isothermal vertical plate, under the action of transversely applied magnetic field has been presented. The plate temperature is raised to Tw and the concentration level near the plate is also raised to C′w . The dimensionless governing equations are solved using Laplace-transform technique. The velocity profiles, temperature and concentration are studied for different physical parameters like thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number and time. It is observed that the velocity increases with increasing values of thermal Grashof number or mass Grashof number. It is also observed that the velocity increases with decreasing magnetic field parameter.

Stability analysis of single-phase thermosyphon loops by finite difference numerical methods

International Nuclear Information System (INIS)

Ambrosini, W.

1998-01-01

In this paper, examples of the application of finite difference numerical methods in the analysis of stability of single-phase natural circulation loops are reported. The problem is here addressed for its relevance for thermal-hydraulic system code applications, in the aim to point out the effect of truncation error on stability prediction. The methodology adopted for analysing in a systematic way the effect of various finite difference discretization can be considered the numerical analogue of the usual techniques adopted for PDE stability analysis. Three different single-phase loop configurations are considered involving various kinds of boundary conditions. In one of these cases, an original dimensionless form of the governing equations is proposed, adopting the Reynolds number as a flow variable. This allows for an appropriate consideration of transition between laminar and turbulent regimes, which is not possible with other dimensionless forms, thus enlarging the field of validity of model assumptions. (author). 14 refs., 8 figs

A correlation for the quench front velocity in the rewetting of a rod by a falling film

International Nuclear Information System (INIS)

Castiglia, F.; Olivieri, E.; Taibi, S.; Vella, G.

1989-01-01

In recent works the exact analytical solutions to the problem of the steady propagation of the quench front in the rewetting by a falling film of both hot vertical slabs and rods have been presented. These solutions furnish the temperature distribution in the solid and, in particular, the dimensioless sputtering temperature, in terms of the Biot number B and the dimensionless front velocity u. As it is well known, however, in practical applications it result more convenient to deal with an explicit - even if approximate - formula which gives the dimensionless rewetting velocity in terms of B and Θ. In view of this, in the present paper, an extension to the case of rods of a simple and reliable correlation for the prediction of the quench front velocity, already proposed for slabs, is presented. Also in this case, the correlation proves fairly satisfactory and confirms its validity in the full range of practical interest the operating parameters

Controlled Roof Collapse during Secondary Mining in Coal Mines

Directory of Open Access Journals (Sweden)

Ashleigh Hutchinson

2012-01-01

Full Text Available The problem considered is an investigation of the possible collapse of the roof between the pillar next to be mined in secondary coal mining and the first line of pillar remnants called snooks. The roof rock between the pillar, which is the working face, and the snook is modelled as an Euler-Bernoulli beam acted on at each end by a horizontal force and by its weight per unit length. The beam is clamped at the pillar and simply supported (hinged at the snook. The dimensionless differential equation for the beam and the boundary conditions depend on one dimensionless number . We consider the range of values of before the displacement and curvature first become singular at =1. The model predicts that for all practical purposes, the beam will break at the clamped end at the pillar. The failure of the beam for values of greater than 1 is investigated computationally.

Quantum entanglement at negative temperature

International Nuclear Information System (INIS)

Furman, G B; Meerovich, V M; Sokolovsky, V L

2013-01-01

An isolated spin system that is in internal thermodynamic equilibrium and that has an upper limit to its allowed energy states can possess a negative temperature. We calculate the thermodynamic characteristics and the concurrence in this system over the entire range of positive and negative temperatures. Our calculation was performed for different real structures, which can be used in experiments. It is found that the temperature dependence of the concurrence is substantially asymmetrical similarly to other thermodynamic characteristics. At a negative temperature the maximum concurrence and the absolute temperature of the entanglement appearance are significantly larger than those at a positive temperature. The concurrence can be characterized by two dimensionless parameters: the ratio between the Zeeman and dipolar energies and the ratio of the thermal and dipolar energies. It was shown that for all considered structures the dimensionless temperatures of the transition between entanglement and separability of the first and second spins are independent of spin structure and the number of spins. (paper)

Short-term gas dispersion in idealised urban canopy in street parallel with flow direction

Science.gov (United States)

Chaloupecká, Hana; Jaňour, Zbyněk; Nosek, Štěpán

2016-03-01

Chemical attacks (e.g. Syria 2014-15 chlorine, 2013 sarine or Iraq 2006-7 chlorine) as well as chemical plant disasters (e.g. Spain 2015 nitric oxide, ferric chloride; Texas 2014 methyl mercaptan) threaten mankind. In these crisis situations, gas clouds are released. Dispersion of gas clouds is the issue of interest investigated in this paper. The paper describes wind tunnel experiments of dispersion from ground level point gas source. The source is situated in a model of an idealised urban canopy. The short duration releases of passive contaminant ethane are created by an electromagnetic valve. The gas cloud concentrations are measured in individual places at the height of the human breathing zone within a street parallel with flow direction by Fast-response Ionisation Detector. The simulations of the gas release for each measurement position are repeated many times under the same experimental set up to obtain representative datasets. These datasets are analysed to compute puff characteristics (arrival, leaving time and duration). The results indicate that the mean value of the dimensionless arrival time can be described as a growing linear function of the dimensionless coordinate in the street parallel with flow direction where the gas source is situated. The same might be stated about the dimensionless leaving time as well as the dimensionless duration, however these fits are worse. Utilising a linear function, we might also estimate some other statistical characteristics from datasets than the datasets means (medians, trimeans). The datasets of the dimensionless arrival time, the dimensionless leaving time and the dimensionless duration can be fitted by the generalized extreme value distribution (GEV) in all sampling positions except one.

Study of ATES thermal behavior using a steady flow model

Science.gov (United States)

Doughty, C.; Hellstroem, G.; Tsang, C. F.; Claesson, J.

1981-01-01

The thermal behavior of a single well aquifer thermal energy storage system in which buoyancy flow is neglected is studied. A dimensionless formulation of the energy transport equations for the aquifer system is presented, and the key dimensionless parameters are discussed. A simple numerical model is used to generate graphs showing the thermal behavior of the system as a function of these parameters. Some comparisons with field experiments are given to illustrate the use of the dimensionless groups and graphs.

Cladding motion and entrainment during loss of flow in the LMFBR

International Nuclear Information System (INIS)

Scale, T.J.; Eggen, D.T.

1978-01-01

The study that has been undertaken here is to characterize the loss of flow with appropriate dimensionless numbers such as Re, sup(p)vap/Psteel, sup(Dh/L), and to suggest a minimum Re, necessary for entrainment of simulant cladding material under transient melting. In particular, we are interested in the downward flow of vapor over an intact rod undergoing a loss of flow or loss of heat sink. (author)

Variational coupling between q-number and c-number dynamics

International Nuclear Information System (INIS)

Amaral, C.M. do; Joffily, S.

1984-01-01

The time-dependent quantum variational principle is generalized for the case of hamiltonian operators having real parameters and their time derivates. The obtained variational system is formed by a Schroedinger equation coupled to a Lagrange equation system, where the lagrangian is the average value of the parametrized hamiltonian operator. The consequent dynamics of the variational principle, describes the interaction between a q-number sub-dynamics with a c-number sub-dynamics. In the ((h/2π)) 0 -order W.K.B. approximation, the variational system reduces to a Hamilton-Jacobi-like equation, coupled to a Lagrange equation family. The formal features of the obtained variational system are appropriated for the description of, adiabatics and non-adiabatics, time-dependent q-number c-number interactions. (L.C.) [pt

Chocolate Numbers

OpenAIRE

Ji, Caleb; Khovanova, Tanya; Park, Robin; Song, Angela

2015-01-01

In this paper, we consider a game played on a rectangular $m \\times n$ gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of taking any piece of chocolate and breaking it again along existing grid lines, until just $mn$ individual squares remain. This paper enumerates the number of ways to break an $m \\times n$ bar, which we call chocolate numbers, and introduces four new sequences related to these numbers. Using various techniques, we p...

Optimal design of multistage chemostats in series using different microbial growth kinetics

Energy Technology Data Exchange (ETDEWEB)

Qasim, Muhammad [Petroleum Engineering Technology, Abu Dhabi Polytechnic (United Arab Emirates)

2013-07-01

In this paper, the optimum design of multistage chemostats (CSTRs) was investigated. The optimal design was based on the minimum overall reactor volume using different volume for each chemostat. The paper investigates three different microbial growth kinetics; Monod kinetics, Contois kinetics and the Logistic equation. The total dimensionless residence time (theta Total) was set as the optimization objective function that was minimized by varying the intermediate dimensionless substrate concentration (alfa i). The effect of inlet substrate concentration (S0) to the first reactor on the optimized total dimensionless residence time was investigated at a constant conversion of 0.90. In addition, the effect of conversion on the optimized total dimensionless residence time was also investigated at constant inlet substrate concentration (S0). For each case, optimization was done using up to five chemostats in series.

The Super Patalan Numbers

OpenAIRE

Richardson, Thomas M.

2014-01-01

We introduce the super Patalan numbers, a generalization of the super Catalan numbers in the sense of Gessel, and prove a number of properties analagous to those of the super Catalan numbers. The super Patalan numbers generalize the super Catalan numbers similarly to how the Patalan numbers generalize the Catalan numbers.

MHD Jeffrey nanofluid past a stretching sheet with viscous dissipation effect

Science.gov (United States)

Zokri, S. M.; Arifin, N. S.; Salleh, M. Z.; Kasim, A. R. M.; Mohammad, N. F.; Yusoff, W. N. S. W.

2017-09-01

This study investigates the influence of viscous dissipation on magnetohydrodynamic (MHD) flow of Jeffrey nanofluid over a stretching sheet with convective boundary conditions. The nonlinear partial differential equations are reduced into the nonlinear ordinary differential equations by utilizing the similarity transformation variables. The Runge-Kutta Fehlberg method is used to solve the problem numerically. The numerical solutions obtained are presented graphically for several dimensionless parameters such as Brownian motion, Lewis number and Eckert number on the specified temperature and concentration profiles. It is noted that the temperature profile is accelerated due to increasing values of Brownian motion parameter and Eckert number. In contrast, both the Brownian motion parameter and Lewis number have caused the deceleration in the concentration profiles.

On the relation between grammatical number and cardinal numbers in development.

Science.gov (United States)

Sarnecka, Barbara W

2014-01-01

This mini-review focuses on the question of how the grammatical number system of a child's language may help the child learn the meanings of cardinal number words (e.g., "one" and "two"). Evidence from young children learning English, Russian, Japanese, Mandarin, Slovenian, or Saudi Arabic suggests that trajectories of number-word learning differ for children learning different languages. Children learning English, which distinguishes between singular and plural, seem to learn the meaning of the cardinal number "one" earlier than children learning Japanese or Mandarin, which have very little singular/plural marking. Similarly, children whose languages have a singular/dual/plural system (Slovenian and Saudi Arabic) learn the meaning of "two" earlier than English-speaking children. This relation between grammatical and cardinal number may shed light on how humans acquire cardinal-number concepts. There is an ongoing debate about whether mental symbols for small cardinalities (concepts for "oneness," "twoness," etc.) are innate or learned. Although an effect of grammatical number on number-word learning does not rule out nativist accounts, it seems more consistent with constructivist accounts, which portray the number-learning process as one that requires significant conceptual change.

Number theory

CERN Document Server

Andrews, George E

1994-01-01

Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simpl

Number Worlds: Visual and Experimental Access to Elementary Number Theory Concepts

Science.gov (United States)

Sinclair, Nathalie; Zazkis, Rina; Liljedahl, Peter

2004-01-01

Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called "Number Worlds" that was designed to support the exploration of elementary number theory concepts by…

Applied number theory

CERN Document Server

Niederreiter, Harald

2015-01-01

This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas.  Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars’ GPS systems, in online banking, etc.  Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters...

On the Relation Between Grammatical Number and Cardinal Numbers in Development

Directory of Open Access Journals (Sweden)

Barbara W Sarnecka

2014-10-01

Full Text Available This mini-review focuses on the question of how the grammatical number system of a child’s language may help the child learn the meanings of cardinal number words (e.g., ‘one’ and ‘two’. Evidence from young children learning English, Russian, Japanese, Mandarin, Slovenian or Saudi Arabic suggests that trajectories of number-word learning differ for children learning different languages. Children learning English, which distinguishes between singular and plural, seem to learn the meaning of the cardinal number ‘one’ earlier than children learning Japanese or Mandarin, which have very little singular/plural marking. Similarly, children whose languages have a singular/dual/plural system (Slovenian and Saudi Arabic learn the meaning of ‘two’ earlier than English-speaking children. This relation between grammatical and cardinal number may shed light on how humans acquire cardinal-number concepts. There is an ongoing debate about whether mental symbols for small cardinalities (concepts for ‘oneness,’ ‘twoness,’ etc. are innate or learned. Although an effect of grammatical number on number-word learning does not rule out nativist accounts, it seems more consistent with constructivist accounts, which portray the number-learning process as one that requires significant conceptual change.

Department of Defense Weapon System Acquisition Policy: A System Dynamics Model and Analysis.

Science.gov (United States)

1982-09-01

dimensionless) PRPRD = Perceived Pressure for R&D (dimensionless) PU - Programs in Progress (programs) RPRD - Raw Pressure for R&D (dimensionless) TDPP - Time...ECAP) TH9 Pressure Ra Pressure_.- for Acquisition ( TDPP ) TH25 4for Acquisition (DPFAO) TH22D (DPPFAO) TH21 US Intelligence \\ - 7 Delay Time / efense...DIBP, DPPFAQ. K) TH22 A CPPFAG.K=DLINF3(RPFAG.KTCPP) TH23 A CPFAQ.K=MAX (DIBPCPPFAQ.K) TH24 C TDPP =12 TH25 C TCPP-24 TH26 CPFAQ Congressional Pressure

Number words and number symbols a cultural history of numbers

CERN Document Server

Menninger, Karl

1992-01-01

Classic study discusses number sequence and language and explores written numerals and computations in many cultures. "The historian of mathematics will find much to interest him here both in the contents and viewpoint, while the casual reader is likely to be intrigued by the author's superior narrative ability.

Numerical solution of non-linear dual-phase-lag bioheat transfer equation within skin tissues.

Science.gov (United States)

Kumar, Dinesh; Kumar, P; Rai, K N

2017-11-01

This paper deals with numerical modeling and simulation of heat transfer in skin tissues using non-linear dual-phase-lag (DPL) bioheat transfer model under periodic heat flux boundary condition. The blood perfusion is assumed temperature-dependent which results in non-linear DPL bioheat transfer model in order to predict more accurate results. A numerical method of line which is based on finite difference and Runge-Kutta (4,5) schemes, is used to solve the present non-linear problem. Under specific case, the exact solution has been obtained and compared with the present numerical scheme, and we found that those are in good agreement. A comparison based on model selection criterion (AIC) has been made among non-linear DPL models when the variation of blood perfusion rate with temperature is of constant, linear and exponential type with the experimental data and it has been found that non-linear DPL model with exponential variation of blood perfusion rate is closest to the experimental data. In addition, it is found that due to absence of phase-lag phenomena in Pennes bioheat transfer model, it achieves steady state more quickly and always predict higher temperature than thermal and DPL non-linear models. The effect of coefficient of blood perfusion rate, dimensionless heating frequency and Kirchoff number on dimensionless temperature distribution has also been analyzed. The whole analysis is presented in dimensionless form. Copyright © 2017 Elsevier Inc. All rights reserved.

Dynamics of an assembly of finite-size Lennard-Jones spheres

International Nuclear Information System (INIS)

Singh, P.

1996-01-01

The time-averaged Fourier spectra of the number density, velocity, and force fields are obtained numerically for an assembly of spherical particles interacting via the Lennard-Jones potential. The magnitude spectra determine the dominant wave numbers, and the phase difference between the Lennard-Jones force and number density spectra determines the nature of the particle dynamics. The latter is used to show that for every wave number k there is a critical frequency ω c (k), such that when ω c (k) the phase difference is π/2 and when ω approx-gt ω c (k) the phase difference is -π/2. The ratio of the frequency and the wave number at which the phase difference changes sign is used to define an effective sound speed for the particle system. The effective sound speed is shown to be a function of the dimensionless wave number, and is locally minimum at the same dimensionless wave numbers for which the static structure factor is minimum. It is also shown that the dynamical response of the particle system for waves with speeds greater than the effective sound speed is similar to the response of the hyperbolic systems of equations, and for waves with speeds smaller than the effective sound speed the response is similar to the response of the elliptic systems. The convection effects are shown to be of the same order of magnitude as the Lennard-Jones forces, and the change of type of the equations from hyperbolic to elliptic occurs when the magnitude of the convection term is comparable to the magnitude of the Lennard-Jones force term. It is also shown that the change of type cannot occur in a theory where the convection term is neglected. copyright 1996 The American Physical Society

Safety-in-numbers

DEFF Research Database (Denmark)

Elvik, Rune; Bjørnskau, Torkel

2017-01-01

Highlights •26 studies of the safety-in-numbers effect are reviewed. •The existence of a safety-in-numbers effect is confirmed. •Results are consistent. •Causes of the safety-in-numbers effect are incompletely known....

Prediction of 222 Rn exhalation rates from phosphogypsum based stacks. Part II: preliminary numerical results

International Nuclear Information System (INIS)

Rabi, Jose A.; Mohamad, Abdulmajeed A.

2004-01-01

The first part of this paper proposes a steady-state 2-D model for 222 Rn transport in phosphogypsum stacks. In this second part, the dimensionless model equations are solved numerically with the help of an existing finite-volume simulator that has been successfully used to solve heat and mass transfer problems in porous media. As a test case, a rectangular shaped stack is considered in order to verify the ability of the proposed parametric approach to account for concurrent effects on the 222 Rn exhalation into the local atmosphere. Air flow is supposed to be strictly buoyancy driven and the ground is assumed to be impermeable to 222 Rn and at a higher temperature under the stack base. Dimensionless controlling parameters are set to representative values and results are presented for Grashof number in the range 10 6 ≤Gr≤ 10 8 , corresponding to very small to small temperature differences between incoming air and ground underneath the stack base. For the particular set of parameters and inasmuch as Gr increases, streamlines presented basically the same pattern while internal isotherms and iso concentration lines remained almost unchanged. Total average Sherwood number proved to be rather insensitive to Gr while total average Nusselt increased slightly with Gr. (author)

Numerical solutions for magnetohydrodynamic flow of nanofluid over a bidirectional non-linear stretching surface with prescribed surface heat flux boundary

International Nuclear Information System (INIS)

Mahanthesh, B.; Gireesha, B.J.; Gorla, R.S. Reddy; Abbasi, F.M.; Shehzad, S.A.

2016-01-01

Numerical solutions of three-dimensional flow over a non-linear stretching surface are developed in this article. An electrically conducting flow of viscous nanoliquid is considered. Heat transfer phenomenon is accounted under thermal radiation, Joule heating and viscous dissipation effects. We considered the variable heat flux condition at the surface of sheet. The governing mathematical equations are reduced to nonlinear ordinary differential systems through suitable dimensionless variables. A well-known shooting technique is implemented to obtain the results of dimensionless velocities and temperature. The obtained results are plotted for multiple values of pertinent parameters to discuss the salient features of these parameters on fluid velocity and temperature. The expressions of skin-friction coefficient and Nusselt number are computed and analyzed comprehensively through numerical values. A comparison of present results with the previous results in absence of nanoparticle volume fraction, mixed convection and magnetic field is computed and an excellent agreement noticed. We also computed the results for both linear and non-linear stretching sheet cases. - Highlights: • Hydromagnetic flow of nanofluid over a bidirectional non-linear stretching surface is examined. • Cu, Al 2 O3 and TiO 2 types nanoparticles are taken into account. • Numerical solutions have been computed and addressed. • The values of skin-friction and Nusselt number are presented.

Boys who pee the farthest have a large hollow head, a thin skin, and medium-size manhood

Science.gov (United States)

Attinger, Daniel; Lee, Vincent

2016-11-01

Following a recent trend of scientific studies on artwork, we study here the thermodynamics of a jetting thermometer made of ceramic, related to the Chinese tea culture. The thermometer represents a boy who "urinates" shortly after hot water is poured onto his head. Long jetting distance indicates if the water temperature is hot enough to brew tea. Here, a thermofluid model describes the jetting phenomenon of that pee-pee boy. The study demonstrates how thermal expansion of an interior air pocket causes jetting. The validity of assumptions underlying the Hagen-Poiseuille flow is discussed for urethra of finite length. A thermodynamic potential is shown to define maximum jetting velocity. Seven optimization criteria to maximize jetting distance are provided, including two dimensionless numbers. The dimensionless numbers are obtained by comparing the time scales of the internal pressure buildup due to heating, with that of pressure relief due to jetting. Optimization results show that longer jets are produced by large individuals, with low body mass index, with a boyhood of medium size inclined at an angle π/4. Analogies are drawn with pissing contests among humans and lobsters. The study ends by noting similitudes of working principle between that politically incorrect thermometer and Galileo Galilei's thermoscope.

Prediction of 222 Rn exhalation rates from phosphogypsum based stacks. Part I: parametric mathematical modeling

International Nuclear Information System (INIS)

Rabi, Jose A.; Mohamad, Abdulmajeed A.

2004-01-01

Radon-222 is a radionuclide exhaled from phosphogypsum by-produced at phosphate fertilizer industries. Alternative large-scale application of this waste may indicate a material substitute for civil engineering provided that environmental issues concerning its disposal and management are overcome. The first part of this paper outlines a steady-state two-dimensional model for 222 Rn transport through porous media, inside which emanation (source term) and decay (sink term) exist. Boussinesq approach is evoked for the laminar buoyancy-driven interstitial air flow, which is also modeled according to Darcy-Brinkman formulation. In order to account for simultaneous effects of entailed physical parameters, governing equations are cast into dimensionless form. Apart from usual controlling parameters like Reynolds, Prandtl, Schmidt, Grashof and Darcy numbers, three unconventional dimensionless groups are put forward. Having in mind 222 Rn transport in phosphogypsum-bearing porous media, the physical meaning of those newly introduced parameters and representative values for the involved physical parameters are presented. A limiting diffusion-dominated scenario is addressed, for which an analytical solution is deduced for boundary conditions including an impermeable phosphogypsum stack base and a non-zero fixed concentration activity at the stack top. Accordingly, an expression for the average Sherwood number corresponding to the normalized 222 Rn exhalation rate is presented

Universal critical wrapping probabilities in the canonical ensemble

Directory of Open Access Journals (Sweden)

Hao Hu

2015-09-01

Full Text Available Universal dimensionless quantities, such as Binder ratios and wrapping probabilities, play an important role in the study of critical phenomena. We study the finite-size scaling behavior of the wrapping probability for the Potts model in the random-cluster representation, under the constraint that the total number of occupied bonds is fixed, so that the canonical ensemble applies. We derive that, in the limit L→∞, the critical values of the wrapping probability are different from those of the unconstrained model, i.e. the model in the grand-canonical ensemble, but still universal, for systems with 2yt−d>0 where yt=1/ν is the thermal renormalization exponent and d is the spatial dimension. Similar modifications apply to other dimensionless quantities, such as Binder ratios. For systems with 2yt−d≤0, these quantities share same critical universal values in the two ensembles. It is also derived that new finite-size corrections are induced. These findings apply more generally to systems in the canonical ensemble, e.g. the dilute Potts model with a fixed total number of vacancies. Finally, we formulate an efficient cluster-type algorithm for the canonical ensemble, and confirm these predictions by extensive simulations.

Local velocity scaling in T400 vessel agitated by Rushton turbine in a fully turbulent region

Science.gov (United States)

Šulc, Radek; Ditl, Pavel; Fořt, Ivan; Jašíkova, Darina; Kotek, Michal; Kopecký, Václav; Kysela, Bohuš

The hydrodynamics and flow field were measured in an agitated vessel using 2-D Time Resolved Particle Image Velocimetry (2-D TR PIV). The experiments were carried out in a fully baffled cylindrical flat bottom vessel 400 mm in inner diameter agitated by a Rushton turbine 133 mm in diameter. The velocity fields were measured in the zone in upward flow to the impeller for impeller rotation speeds from 300 rpm to 850 rpm and three liquids of different viscosities (i.e. (i) distilled water, ii) a 28% vol. aqueous solution of glycol, and iii) a 43% vol. aqueous solution of glycol), corresponding to the impeller Reynolds number in the range 50 000 < Re < 189 000. This Re range secures the fully-developed turbulent flow of agitated liquid. In accordance with the theory of mixing, the dimensionless mean and fluctuation velocities in the measured directions were found to be constant and independent of the impeller Reynolds number. On the basis of the test results the spatial distributions of dimensionless velocities were calculated. The axial turbulence intensity was found to be in the majority in the range from 0.388 to 0.540, which corresponds to the high level of turbulence intensity.

Local velocity scaling in T400 vessel agitated by Rushton turbine in a fully turbulent region

Directory of Open Access Journals (Sweden)

Šulc Radek

2017-01-01

Full Text Available The hydrodynamics and flow field were measured in an agitated vessel using 2-D Time Resolved Particle Image Velocimetry (2-D TR PIV. The experiments were carried out in a fully baffled cylindrical flat bottom vessel 400 mm in inner diameter agitated by a Rushton turbine 133 mm in diameter. The velocity fields were measured in the zone in upward flow to the impeller for impeller rotation speeds from 300 rpm to 850 rpm and three liquids of different viscosities (i.e. (i distilled water, ii a 28% vol. aqueous solution of glycol, and iii a 43% vol. aqueous solution of glycol, corresponding to the impeller Reynolds number in the range 50 000 < Re < 189 000. This Re range secures the fully-developed turbulent flow of agitated liquid. In accordance with the theory of mixing, the dimensionless mean and fluctuation velocities in the measured directions were found to be constant and independent of the impeller Reynolds number. On the basis of the test results the spatial distributions of dimensionless velocities were calculated. The axial turbulence intensity was found to be in the majority in the range from 0.388 to 0.540, which corresponds to the high level of turbulence intensity.

Wavenumber Spectrum of Intermediate-Scale Ocean Surface Waves

National Research Council Canada - National Science Library

Hwang, Paul A

2005-01-01

... (wavelengths between 0.02 and 6 m) under various sea-state conditions. The main result of the analysis is that the dependence of the dimensionless wave spectrum on the dimensionless wind friction velocity follows a power-law function...

Gaussian beam profile shaping apparatus, method therefore and evaluation thereof

International Nuclear Information System (INIS)

Dickey, F.M.; Holswade, S.C.; Romero, L.A.

1999-01-01

A method and apparatus maps a Gaussian beam into a beam with a uniform irradiance profile by exploiting the Fourier transform properties of lenses. A phase element imparts a design phase onto an input beam and the output optical field from a lens is then the Fourier transform of the input beam and the phase function from the phase element. The phase element is selected in accordance with a dimensionless parameter which is dependent upon the radius of the incoming beam, the desired spot shape, the focal length of the lens and the wavelength of the input beam. This dimensionless parameter can also be used to evaluate the quality of a system. In order to control the radius of the incoming beam, optics such as a telescope can be employed. The size of the target spot and the focal length can be altered by exchanging the transform lens, but the dimensionless parameter will remain the same. The quality of the system, and hence the value of the dimensionless parameter, can be altered by exchanging the phase element. The dimensionless parameter provides design guidance, system evaluation, and indication as to how to improve a given system. 27 figs

Damage Evaluation of Critical Components of Tilted Support Spring Nonlinear System under a Rectangular Pulse

Directory of Open Access Journals (Sweden)

Ningning Duan

2015-01-01

Full Text Available Dimensionless nonlinear dynamical equations of a tilted support spring nonlinear packaging system with critical components were obtained under a rectangular pulse. To evaluate the damage characteristics of shocks to packaged products with critical components, a concept of the damage boundary surface was presented and applied to a titled support spring system, with the dimensionless critical acceleration of the system, the dimensionless critical velocity, and the frequency parameter ratio of the system taken as the three basic parameters. Based on the numerical results, the effects of the frequency parameter ratio, the mass ratio, the dimensionless peak pulse acceleration, the angle of the system, and the damping ratio on the damage boundary surface of critical components were discussed. It was demonstrated that with the increase of the frequency parameter ratio, the decrease of the angle, and/or the increase of the mass ratio, the safety zone of critical components can be broadened, and increasing the dimensionless peak pulse acceleration or the damping ratio may lead to a decrease of the damage zone for critical components. The results may lead to a thorough understanding of the design principles for the tilted support spring nonlinear system.

Predicting Lotto Numbers

DEFF Research Database (Denmark)

Jørgensen, Claus Bjørn; Suetens, Sigrid; Tyran, Jean-Robert

numbers based on recent drawings. While most players pick the same set of numbers week after week without regards of numbers drawn or anything else, we find that those who do change, act on average in the way predicted by the law of small numbers as formalized in recent behavioral theory. In particular......We investigate the “law of small numbers” using a unique panel data set on lotto gambling. Because we can track individual players over time, we can measure how they react to outcomes of recent lotto drawings. We can therefore test whether they behave as if they believe they can predict lotto......, on average they move away from numbers that have recently been drawn, as suggested by the “gambler’s fallacy”, and move toward numbers that are on streak, i.e. have been drawn several weeks in a row, consistent with the “hot hand fallacy”....

Transfinite Numbers

Indian Academy of Sciences (India)

Transfinite Numbers. What is Infinity? S M Srivastava. In a series of revolutionary articles written during the last quarter of the nineteenth century, the great Ger- man mathematician Georg Cantor removed the age-old mistrust of infinity and created an exceptionally beau- tiful and useful theory of transfinite numbers. This is.

A benchmark study for the crown-type splashing dynamics of one- and two-component droplet wall-film interactions

Science.gov (United States)

Geppert, A.; Terzis, A.; Lamanna, G.; Marengo, M.; Weigand, B.

2017-12-01

The present paper investigates experimentally the impact dynamics of crown-type splashing for miscible two- and one-component droplet wall-film interactions over a range of Weber numbers and dimensionless film thicknesses. The splashing outcome is parametrised in terms of a set of quantifiable parameters, such as crown height, top and base diameter, wall inclination, number of fingers, and secondary droplet properties. The results show that the outcome of a splashing event is not affected by the choice of similar or dissimilar fluids, provided the dimensionless film thickness is larger than 0.1. Below this threshold, distinctive features of two-component interactions appear, such as hole formation and crown bottom breakdown. The observation of different crown shapes (e.g. V-shaped, cylindrical, and truncated-cone) confirms that vorticity production induces changes in the crown wall inclination, thus affecting the evolution of the crown height and top diameter. The evolution of the crown base diameter, instead, is mainly dependent on the relative importance of liquid inertia and viscous losses in the wall-film. The maximum number of liquid fingers decreases with increasing wall, film thickness, due to the enhanced attenuation of the effect of surface properties on the fingering process. The formation of secondary droplets is also affected by changes in the crown wall inclination. In particular, for truncated-cone shapes the occurrence of crown rim contraction induces a large scatter in the secondary droplet properties. Consequently, empirical models for the maximum number and mean diameter of the secondary droplets are derived for V-shaped crowns, as observed for the hexadecane-Hyspin interactions.

Number in Dinka

DEFF Research Database (Denmark)

Andersen, Torben

2014-01-01

had a marked singular and an unmarked plural. Synchronically, however, the singular is arguably the basic member of the number category as revealed by the use of the two numbers. In addition, some nouns have a collective form, which is grammatically singular. Number also plays a role...

Untitled

Indian Academy of Sciences (India)

number K = kH for the fundamental Love mode for various values of the anisotropy parameters. The curye corresponding to g = 0 is for isotropic media. The phase velocity lies in the range. (1 – e)” < C < 1.3(1 − s.)”. K = 0 for c = (1-s)”; K – co as C– 13(1-3)”. where C = c/6, is the dimensionless phase velocity, K = kH is the ...

Analogy of convective heat transfer between developing laminar secondary flows in pipes

OpenAIRE

Ishigaki, Hiroshi; 石垣　博

1998-01-01

Analogy of convective heat transfer between developing laminar flows in curved pipes and orthogonally rotating pipes is described through similarity arguments and numerical computation. Governing parameters and a dimensionless axial distance are properly used for the respective flows. When the second parameter is large in each flow, it is shown that the temperature profiles and the Nusselt numbers of the two flows are approximately similar for the same values of the governing parameter, Prand...

The effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer of upper-convected Maxwell fluid in the presence of nanoparticle past a stretching sheet

Directory of Open Access Journals (Sweden)

Wubshet Ibrahim

2016-06-01

The numerical results are obtained for velocity, temperature, induced magnetic field and concentration profiles as well as skin friction coefficient, the local Nusselt number and Sherwood number. The results indicate that the skin friction coefficient, the local Nusselt number and Sherwood number decrease with an increase in B and M parameters. Moreover, local Sherwood number -ϕ′(0 decreases with an increase in convective parameter Bi, but the local Nusselt number -θ′(0 increases with an increase in Bi. The results are displayed both in graphical and tabular form to illustrate the effect of the governing parameters on the dimensionless velocity, induced magnetic field, temperature and concentration. The numerical results are compared and found to be in good agreement with the previously published results on special cases of the problem.

Heat transfer enhancement by additive in vertical falling film absorption of H2O/LiBr

International Nuclear Information System (INIS)

Cheng Wenlong; Houda, Kouichi; Chen Zeshao; Akisawa, Atsushi; Hu Peng; Kashiwagi, Takao

2004-01-01

The enhancement effects of additive on vertical falling film of water into aqueous lithium bromide (LiBr) were studied by an experimental method. Based on the Navier-Stokes equations of falling film absorption, a new dimensionless parameter, surface renewal number Rn, was introduced, and a semi-empirical equation of enhancement factor of additive was obtained. It was shown that the absorption Marangoni number Ma, the surface Marangoni number M aA , and the surface renewal number Rn enhance the heat transfer of absorption, however the adsorption number Π and the Reynolds number Re weaken the heat transfer of absorption. It was proved that the semi-empirical equation agreed well with the experimental results by introduction of the parameters related to surface tension characters presented by the authors into the equation

On powerful numbers

Directory of Open Access Journals (Sweden)

R. A. Mollin

1986-01-01

Full Text Available A powerful number is a positive integer n satisfying the property that p2 divides n whenever the prime p divides n; i.e., in the canonical prime decomposition of n, no prime appears with exponent 1. In [1], S.W. Golomb introduced and studied such numbers. In particular, he asked whether (25,27 is the only pair of consecutive odd powerful numbers. This question was settled in [2] by W.A. Sentance who gave necessary and sufficient conditions for the existence of such pairs. The first result of this paper is to provide a generalization of Sentance's result by giving necessary and sufficient conditions for the existence of pairs of powerful numbers spaced evenly apart. This result leads us naturally to consider integers which are representable as a proper difference of two powerful numbers, i.e. n=p1−p2 where p1 and p2 are powerful numbers with g.c.d. (p1,p2=1. Golomb (op.cit. conjectured that 6 is not a proper difference of two powerful numbers, and that there are infinitely many numbers which cannot be represented as a proper difference of two powerful numbers. The antithesis of this conjecture was proved by W.L. McDaniel [3] who verified that every non-zero integer is in fact a proper difference of two powerful numbers in infinitely many ways. McDaniel's proof is essentially an existence proof. The second result of this paper is a simpler proof of McDaniel's result as well as an effective algorithm (in the proof for explicitly determining infinitely many such representations. However, in both our proof and McDaniel's proof one of the powerful numbers is almost always a perfect square (namely one is always a perfect square when n≢2(mod4. We provide in §2 a proof that all even integers are representable in infinitely many ways as a proper nonsquare difference; i.e., proper difference of two powerful numbers neither of which is a perfect square. This, in conjunction with the odd case in [4], shows that every integer is representable in

Quantum random-number generator based on a photon-number-resolving detector

International Nuclear Information System (INIS)

Ren Min; Wu, E; Liang Yan; Jian Yi; Wu Guang; Zeng Heping

2011-01-01

We demonstrated a high-efficiency quantum random number generator which takes inherent advantage of the photon number distribution randomness of a coherent light source. This scheme was realized by comparing the photon flux of consecutive pulses with a photon number resolving detector. The random bit generation rate could reach 2.4 MHz with a system clock of 6.0 MHz, corresponding to a random bit generation efficiency as high as 40%. The random number files passed all the stringent statistical tests.

Heat and mass transfer effects on moving vertical plate in the presence of thermal radiation

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2004-01-01

Full Text Available Thermal radiation effects on moving infinite vertical plate in the presence variable temperature and mass diffusion is considered. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The plate temperature and the concentration level near the plate are raised linearly with time. The dimensionless governing equations are solved using the Laplace-transform technique. The velocity and skin-friction are studied for different parameters like thermal Grashof number, mass Grashof number, time and radiation parameter. It is observed that the velocity slightly decreases with increasing value of the radiation parameter.

Correlation to predict heat transfer of an oscillating loop heat pipe consisting of three interconnected columns

International Nuclear Information System (INIS)

Arslan, Goekhan; Ozdemir, Mustafa

2008-01-01

In this paper, heat transfer in an oscillating loop heat pipe is investigated experimentally. The oscillation of the liquid columns at the evaporator and condenser sections of the heat pipe are driven by gravitational force and the phase lag between evaporation and condensation because the dimensions of the heat pipe are large enough to neglect the effect of capillary forces. The overall heat transfer coefficient based on the temperature difference between the evaporator and condenser surfaces is introduced by a correlation function of dimensionless numbers such as kinetic Reynolds number, c p ΔT/h fg and the geometric parameters

Torque scaling in small-gap Taylor-Couette flow with smooth or grooved wall

Science.gov (United States)

Zhu, Bihai; Ji, Zengqi; Lou, Zhengkun; Qian, Pengcheng

2018-03-01

The torque in the Taylor-Couette flow for radius ratios η ≥0.97 , with smooth or grooved wall static outer cylinders, is studied experimentally, with the Reynolds number of the inner cylinder reaching up to Rei=2 ×105 , corresponding to the Taylor number up to Ta =5 ×1010 . The grooves are perpendicular to the mean flow, and similar to the structure of a submersible motor stator. It is found that the dimensionless torque G , at a given Rei and η , is significantly greater for grooved cases than smooth cases. We compare our experimental torques for the smooth cases to the fit proposed by Wendt [F. Wendt, Ing.-Arch. 4, 577 (1993), 10.1007/BF02084936] and the fit proposed by Bilgen and Boulos [E. Bilgen and R. Boulos, J Fluids Eng. 95, 122 (1973), 10.1115/1.3446944], which shows both fits are outside their range for small gaps. Furthermore, an additional dimensionless torque (angular velocity flux) N uω in the smooth cases exhibits an effective scaling of N uω˜T a0.39 in the ultimate regime, which occurs at a lower Taylor number, Ta ≈3.5 ×107 , than the well-explored η =0.714 case (at Ta ≈3 ×108 ). The same effective scaling exponent, 0.39, is also evident in the grooved cases, but for η =0.97 and 0.985, there is a peak before this exponent appears.

Deformation of a Capsule in a Power-Law Shear Flow

Directory of Open Access Journals (Sweden)

Fang-Bao Tian

2016-01-01

Full Text Available An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid. In this method, the flexible structure (e.g., capsule dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.

Nonlinear theory of nonstationary low Mach number channel flows of freely cooling nearly elastic granular gases.

Science.gov (United States)

Meerson, Baruch; Fouxon, Itzhak; Vilenkin, Arkady

2008-02-01

We employ hydrodynamic equations to investigate nonstationary channel flows of freely cooling dilute gases of hard and smooth spheres with nearly elastic particle collisions. This work focuses on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes and employing Lagrangian coordinates, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation becomes exactly soluble, and the solution develops a finite-time density blowup. The blowup has the same local features at singularity as those exhibited by the recently found family of exact solutions of the full set of ideal hydrodynamic equations [I. Fouxon, Phys. Rev. E 75, 050301(R) (2007); I. Fouxon,Phys. Fluids 19, 093303 (2007)]. The heat diffusion, however, always becomes important near the attempted singularity. It arrests the density blowup and brings about previously unknown inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. The ICSs represent exact solutions of the full set of granular hydrodynamic equations. Both the density profile of an ICS and the characteristic relaxation time toward it are determined by a single dimensionless parameter L that describes the relative role of the inelastic energy loss and heat diffusion. At L>1 the intermediate cooling dynamics proceeds as a competition between "holes": low-density regions of the gas. This competition resembles Ostwald

Discovery: Prime Numbers

Science.gov (United States)

de Mestre, Neville

2008-01-01

Prime numbers are important as the building blocks for the set of all natural numbers, because prime factorisation is an important and useful property of all natural numbers. Students can discover them by using the method known as the Sieve of Eratosthenes, named after the Greek geographer and astronomer who lived from c. 276-194 BC. Eratosthenes…

Untitled

Indian Academy of Sciences (India)

, A, to model input, q},. Sp particle surface area, mi,. T temperature, K,. Tm mean temperature, (T + 6T)/(1 +6),. U overall heat transfer coefficient, J/mº K s, dimensionless temperature, T/T., maximum value of dimensionless temperature. y mean ...

Experimental constraints on transport from dimensionless parameter scaling studies

International Nuclear Information System (INIS)

Petty, C.C.; Luce, T.C.; Baker, D.R.; Ballet, B.; Carlstrom, T.N.; Cordey, J.G.; DeBoo, J.C.; Gohil, P.; Groebner, R.J.; Rice, B.W.; Thomas, D.M.; Wade, M.R.; Waltz, R.E.

1998-01-01

The scalings of heat transport with safety factor (q), normalized collisionality (ν), plasma beta (β), and relative gyroradius (ρ * ) have been measured on the DIII-D tokamak [Fusion Technol. 8, 441 (1985)]. The measured ρ * , β and ν scalings of heat transport indicate that ExB transport from drift wave turbulence is a plausible basis for anomalous transport. For high confinement (H) mode plasmas where the safety factor was varied at fixed magnetic shear, the effective (or one-fluid) thermal diffusivity was found to scale like χ eff ∝q 2.3±0.64 , with the ion and electron fluids having the same q scaling to within the experimental errors except near the plasma edge. The scaling of the thermal confinement time with safety factor was in good agreement with this local transport dependence, τ th ∝q -2.42±0.31 ; however, when the magnetic shear was allowed to vary to keep q 0 fixed during the (edge) safety factor scan, a weaker global dependence was observed, τ th ∝q 95 -1.43±0.23 . This weaker dependence was mainly due to the change in the local value of q between the two types of scans. The combined ρ * , β , ν and q scalings of heat transport for H-mode plasmas on DIII-D reproduce the empirical confinement scaling using physical (dimensional) parameters with the exception of weaker power degradation. copyright 1998 American Institute of Physics

Modeling of similar economies

Directory of Open Access Journals (Sweden)

Sergey B. Kuznetsov

2017-06-01

Full Text Available Objective to obtain dimensionless criteria ndash economic indices characterizing the national economy and not depending on its size. Methods mathematical modeling theory of dimensions processing statistical data. Results basing on differential equations describing the national economy with the account of economical environment resistance two dimensionless criteria are obtained which allow to compare economies regardless of their sizes. With the theory of dimensions we show that the obtained indices are not accidental. We demonstrate the implementation of the obtained dimensionless criteria for the analysis of behavior of certain countriesrsquo economies. Scientific novelty the dimensionless criteria are obtained ndash economic indices which allow to compare economies regardless of their sizes and to analyze the dynamic changes in the economies with time. nbsp Practical significance the obtained results can be used for dynamic and comparative analysis of different countriesrsquo economies regardless of their sizes.

The effect of the cranial bone CT numbers on the brain CT numbers

Energy Technology Data Exchange (ETDEWEB)

Fukuda, Hitoshi; Kobayashi, Shotai; Koide, Hiromi; Yamaguchi, Shuhei; Okada, Kazunori; Shimote, Koichi; Tsunematsu, Tokugoro (Shimane Medical Univ., Izumo (Japan))

1989-06-01

The effects of the cranial size and the computed tomography (CT) numbers of the cranial bone on that of the brain were studied in 70 subjects, aged from 30 to 94 years. The subjects had no histories of cerebrovascular accidents and showed no abnormalities in the central nervous system upon physical examinations and a CT scan. We measured the average attenuation values (CT numbers) of each elliptical region (165 pixels, 0.39 cm{sup 2}) at the bilateral thalamus and at twelve areas of the deep white matter. Multiple regression analysis was used to assess the effects of age, cranial size, and cranial bone CT numbers on the brain CT numbers. The effect of the cranial bone CT numbers on the brain CT numbers was statistically significant. The brain CT numbers increased with the increase in the cranial bone CT numbers. There was, however, no significant correlation between brain CT numbers and cranial size. In measuring the brain CT numbers, it is desirable that consideration be given to the cranial bone CT numbers. (author).

A new pseudorandom number generator based on a complex number chaotic equation

International Nuclear Information System (INIS)

Liu Yang; Tong Xiao-Jun

2012-01-01

In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandom number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties

On the number of special numbers

Indian Academy of Sciences (India)

without loss of any generality to be the first k primes), then the equation a + b = c has .... This is an elementary exercise in partial summation (see [12]). Thus ... This is easily done by inserting a stronger form of the prime number theorem into the.

Numerical simulation of jet breakup behavior by the lattice Boltzmann method

International Nuclear Information System (INIS)

Matsuo, Eiji; Koyama, Kazuya; Abe, Yutaka; Iwasawa, Yuzuru; Ebihara, Ken-ichi

2015-01-01

In order to understand the jet breakup behavior of the molten core material into coolant during a core disruptive accident (CDA) for a sodium-cooled fast reactor (SFR), we simulated the jet breakup due to the hydrodynamic interaction using the lattice Boltzmann method (LBM). The applicability of the LBM to the jet breakup simulation was validated by comparison with our experimental data. In addition, the influence of several dimensionless numbers such as Weber number and Froude number was examined using the LBM. As a result, we validated applicability of the LBM to the jet breakup simulation, and found that the jet breakup length is independent of Froude number and in good agreement with the Epstein's correlation when the jet interface becomes unstable. (author)

Predicting Lotto Numbers

DEFF Research Database (Denmark)

Suetens, Sigrid; Galbo-Jørgensen, Claus B.; Tyran, Jean-Robert Karl

2016-01-01

We investigate the ‘law of small numbers’ using a data set on lotto gambling that allows us to measure players’ reactions to draws. While most players pick the same set of numbers week after week, we find that those who do change react on average as predicted by the law of small numbers...... as formalized in recent behavioral theory. In particular, players tend to bet less on numbers that have been drawn in the preceding week, as suggested by the ‘gambler’s fallacy’, and bet more on a number if it was frequently drawn in the recent past, consistent with the ‘hot-hand fallacy’....

Scrutiny of underdeveloped nanofluid MHD flow and heat conduction in a channel with porous walls

Directory of Open Access Journals (Sweden)

M. Fakour

2014-11-01

Full Text Available In this paper, laminar fluid flow and heat transfer in channel with permeable walls in the presence of a transverse magnetic field is investigated. Least square method (LSM for computing approximate solutions of nonlinear differential equations governing the problem. We have tried to show reliability and performance of the present method compared with the numerical method (Runge–Kutta fourth-rate to solve this problem. The influence of the four dimensionless numbers: the Hartmann number, Reynolds number, Prandtl number and Eckert number on non-dimensional velocity and temperature profiles are considered. The results show analytical present method is very close to numerically method. In general, increasing the Reynolds and Hartman number is reduces the nanofluid flow velocity in the channel and the maximum amount of temperature increase and increasing the Prandtl and Eckert number will increase the maximum amount of theta.

Study of heat transfer and flow of nanofluid in permeable channel in the presence of magnetic field

Directory of Open Access Journals (Sweden)

M. Fakour

2015-03-01

Full Text Available In this paper, laminar fluid flow and heat transfer in channel with permeable walls in the presence of a transverse magnetic field is investigated. Least square method (LSM for computing approximate solutions of nonlinear differential equations governing the problem. We have tried to show reliability and performance of the present method compared with the numerical method (Runge-Kutta fourth-rate to solve this problem. The influence of the four dimensionless numbers: the Hartmann number, Reynolds number, Prandtl number and Eckert number on non-dimensional velocity and temperature profiles are considered. The results show analytical present method is very close to numerically method. In general, increasing the Reynolds and Hartman number is reduces the nanofluid flow velocity in the channel and the maximum amount of temperature increase and increasing the Prandtl and Eckert number will increase the maximum amount of theta.

Spatial displacement of numbers on a vertical number line in spatial neglect

Directory of Open Access Journals (Sweden)

Urszula eMihulowicz

2015-04-01

Full Text Available Previous studies that investigated the association of numbers and space in humans came to contradictory conclusions about the spatial character of the mental number magnitude representation and about how it may be influenced by unilateral spatial neglect. The present study aimed to disentangle the debated influence of perceptual versus representational aspects via explicit mapping of numbers onto space by applying the number line estimation paradigm with vertical orientation of stimulus lines. Thirty-five acute right-brain damaged stroke patients (6 with neglect were asked to place two-digit numbers on vertically oriented lines with 0 marked at the bottom and 100 at the top. In contrast to the expected, nearly linear mapping in the control patient group, patients with spatial neglect overestimated the position of numbers in the lower middle range. The results corroborate spatial characteristics of the number magnitude representation. In neglect patients, this representation seems to be biased towards the ipsilesional side, independent of the physical orientation of the task stimuli.

Exact solution of thermal radiation on vertical oscillating plate with variable temperature and mass flux

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2010-01-01

Full Text Available Thermal radiation effects on unsteady flow past an infinite vertical oscillating plate in the presence of variable temperature and uniform mass flux is considered. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The plate temperature is raised linearly with time and the mass is diffused from the plate to the fluid at an uniform rate. The dimensionless governing equations are solved using the Laplace transform technique. The velocity, concentration and temperature are studied for different physical parameters like the phase angle, radiation parameter, Schmidt number, thermal Grashof number, mass Grashof number and time. It is observed that the velocity increases with decreasing phase angle ωt.

Radiation effects on flow past an impulsively started vertical plate with variable temperature and mass flux

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2005-01-01

Full Text Available An analysis is performed to study the thermal radiation effects on unsteady free convective flow over a moving vertical plate in the presence of variable temperature and uniform mass flux. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The temperature is raised linearly with time and the concentration level near the plate are raised linearly with time. The dimensionless governing equations are solved using the Laplace transform technique. The velocity and skinfriction are studied for different parameters like the radiation parameter, Schmidt number, thermal Grashof number, mass Grashof number and time. It is observed that the velocity increases with decreasing radiation parameter.

Forecasting production in Liquid Rich Shale plays

Science.gov (United States)

Nikfarman, Hanieh

Production from Liquid Rich Shale (LRS) reservoirs is taking center stage in the exploration and production of unconventional reservoirs. Production from the low and ultra-low permeability LRS plays is possible only through multi-fractured horizontal wells (MFHW's). There is no existing workflow that is applicable to forecasting multi-phase production from MFHW's in LRS plays. This project presents a practical and rigorous workflow for forecasting multiphase production from MFHW's in LRS reservoirs. There has been much effort in developing workflows and methodology for forecasting in tight/shale plays in recent years. The existing workflows, however, are applicable only to single phase flow, and are primarily used in shale gas plays. These methodologies do not apply to the multi-phase flow that is inevitable in LRS plays. To account for complexities of multiphase flow in MFHW's the only available technique is dynamic modeling in compositional numerical simulators. These are time consuming and not practical when it comes to forecasting production and estimating reserves for a large number of producers. A workflow was developed, and validated by compositional numerical simulation. The workflow honors physics of flow, and is sufficiently accurate while practical so that an analyst can readily apply it to forecast production and estimate reserves in a large number of producers in a short period of time. To simplify the complex multiphase flow in MFHW, the workflow divides production periods into an initial period where large production and pressure declines are expected, and the subsequent period where production decline may converge into a common trend for a number of producers across an area of interest in the field. Initial period assumes the production is dominated by single-phase flow of oil and uses the tri-linear flow model of Erdal Ozkan to estimate the production history. Commercial software readily available can simulate flow and forecast production in this

Modeling the effect of the inclination angle on natural convection from a flat plate: The case of a photovoltaic module

OpenAIRE

Perović Bojan D.; Klimenta Jelena Lj.; Tasić Dragan S.; Peuteman Joan L.G.; Klimenta Dardan O.; Anđelković Ljiljana N.

2017-01-01

The main purpose of this paper is to show how the inclination angle affects natural convection from a flat-plate photovoltaic module which is mounted on the ground surface. In order to model this effect, novel correlations for natural convection from isothermal flat plates are developed by using the fundamental dimensionless number. On the basis of the available experimental and numerical results, it is shown that the natural convection correlations correspond well with the existing empirical...

New topological structures of Skyrme theory: baryon number and monopole number

Energy Technology Data Exchange (ETDEWEB)

Cho, Y.M. [Chinese Academy of Science, Institute of Modern Physics, Lanzhou (China); Konkuk University, Seoul (Korea, Republic of); Seoul National University, School of Physics and Astronomy, Seoul (Korea, Republic of); Kimm, Kyoungtae [Seoul National University, Faculty of Liberal Education, Seoul (Korea, Republic of); Yoon, J.H. [Konkuk University, Department of Physics, Seoul (Korea, Republic of); Zhang, Pengming [Chinese Academy of Science, Institute of Modern Physics, Lanzhou (China)

2017-02-15

Based on the observation that the skyrmion in Skyrme theory can be viewed as a dressed monopole, we show that the skyrmions have two independent topology, the baryon topology π{sub 3}(S{sup 3}) and the monopole topology π{sub 2}(S{sup 2}). With this we propose to classify the skyrmions by two topological numbers (m, n), the monopole number m and the shell (radial) number n. In this scheme the popular (non spherically symmetric) skyrmions are classified as the (m, 1) skyrmions but the spherically symmetric skyrmions are classified as the (1, n) skyrmions, and the baryon number B is given by B = mn. Moreover, we show that the vacuum of the Skyrme theory has the structure of the vacuum of the Sine-Gordon theory and QCD combined together, which can also be classified by two topological numbers (p, q). This puts the Skyrme theory in a totally new perspective. (orig.)

Searching fundamental information in ordinary differential equations. Nondimensionalization technique.

Science.gov (United States)

Sánchez Pérez, J F; Conesa, M; Alhama, I; Alhama, F; Cánovas, M

2017-01-01

Classical dimensional analysis and nondimensionalization are assumed to be two similar approaches in the search for dimensionless groups. Both techniques, simplify the study of many problems. The first approach does not need to know the mathematical model, being sufficient a deep understanding of the physical phenomenon involved, while the second one begins with the governing equations and reduces them to their dimensionless form by simple mathematical manipulations. In this work, a formal protocol is proposed for applying the nondimensionalization process to ordinary differential equations, linear or not, leading to dimensionless normalized equations from which the resulting dimensionless groups have two inherent properties: In one hand, they are physically interpreted as balances between counteracting quantities in the problem, and on the other hand, they are of the order of magnitude unity. The solutions provided by nondimensionalization are more precise in every case than those from dimensional analysis, as it is illustrated by the applications studied in this work.

Computational solutions for non-isothermal, nonlinear magneto-convection in porous media with hall/ionslip currents and ohmic dissipation

Directory of Open Access Journals (Sweden)

O. Anwar Bég

2016-03-01

Full Text Available A theoretical and numerical study is presented to analyze the nonlinear, non-isothermal, magnetohydrodynamic (MHD free convection boundary layer flow and heat transfer in a non-Darcian, isotropic, homogenous porous medium, in the presence of Hall currents, Ionslip currents, viscous heating and Joule heating. A power-law variation is used for the temperature at the wall. The governing nonlinear coupled partial differential equations for momentum conservation in the x and z directions and heat conservation, in the flow regime are transformed from an (x, y, z coordinate system to a (ξ,η coordinate system in terms of dimensionless x-direction velocity (∂F/∂η and z-direction velocity (G and dimensionless temperature function (H under appropriate boundary conditions. Both Darcian and Forchheimer porous impedances are incorporated in both momentum equations. Computations are also provided for the variation of the x and z direction shear stress components and also local Nusselt number. Excellent correlation is achieved with a Nakamura tridiagonal finite difference scheme (NTM. The model finds applications in magnetic materials processing, MHD power generators and purification of crude oils.

Prediction of Equilibrium States of Kinematic and Thermal Fields in Homogeneous Turbulence Submitted To the Rotation

International Nuclear Information System (INIS)

Chebbi, Besma; Bouzaiane, Mounir; Lili, Taieb

2009-01-01

In this work, effects of rotation on the evolution of kinematic and thermal fields in homogeneous sheared turbulence are investigated using second order closure modeling. The Launder-Reece-Ro di models, the Speziale-Sarkar-Gatski model and the Shih-Lumley models are retained for pressure-strain correlation and pressure-temperature correlation. Whereas classic models are retained for time evolution equations of kinematic and thermal dissipation rates. The fourth order Runge-Kutta method is used to resolve three non linear differential systems obtained after modeling. The numerical integration is carried out separately for several values of the dimensionless rotation number R equal to 0, 0.25 and 0.5. The obtained results are compared to the recent results of Direct Numerical Simulations of G.Brethouwer. The results have confirmed the asymptotic equilibrium behaviors of kinematic and thermal dimensionless parameters. Furthermore they have shown that rotation affects not only kinematic field but also thermal field. The coupling between the Speziale-Sarkar-Gatski model and the Launder-Reece-Rodi model is of a big contribution on the prediction of kinematic and thermal fields

Prediction of EMP cavitation threshold from other than sodium testing

International Nuclear Information System (INIS)

Kambe, M.; Kamei, M.

2002-01-01

An experimental study has been performed to predict the cavitation threshold of electromagnetic pumps from measurements on test models using water and alcohol. Cavitation tests were carried out using water and alcohol test loop on subscale ducts of transparent acrylic resin with reference to an actual pump (1.1m 3 /min). These data were compared to those obtained from the in-sodium tests on the actual pump. The investigation revealed that the value of Thoma's dimensionless parameter: σ applied to the test model for water and alcohol is quite higher than that of corresponding σ on the actual pump. To minimize the incipient cavitation safety margin, more accurate prediction must be required. In view of this, the authors proposed the dimensionless parameter: σ T =σ/W-bare where W-bare denotes the Weber number. This parameter was confirmed to predict the cavitation threshold of electromagnetic pumps with much more accuracy than ever before. It can also be adopted to predict cavitation threshold of other FBR components. (author)

Path covering number and L(2,1)-labeling number of graphs

OpenAIRE

Lu, Changhong; Zhou, Qing

2012-01-01

A {\\it path covering} of a graph $G$ is a set of vertex disjoint paths of $G$ containing all the vertices of $G$. The {\\it path covering number} of $G$, denoted by $P(G)$, is the minimum number of paths in a path covering of $G$. An {\\sl $k$-L(2,1)-labeling} of a graph $G$ is a mapping $f$ from $V(G)$ to the set ${0,1,...,k}$ such that $|f(u)-f(v)|\\ge 2$ if $d_G(u,v)=1$ and $|f(u)-f(v)|\\ge 1$ if $d_G(u,v)=2$. The {\\sl L(2,1)-labeling number $\\lambda (G)$} of $G$ is the smallest number $k$ suc...

Report number codes

Energy Technology Data Exchange (ETDEWEB)

Nelson, R.N. (ed.)

1985-05-01

This publication lists all report number codes processed by the Office of Scientific and Technical Information. The report codes are substantially based on the American National Standards Institute, Standard Technical Report Number (STRN)-Format and Creation Z39.23-1983. The Standard Technical Report Number (STRN) provides one of the primary methods of identifying a specific technical report. The STRN consists of two parts: The report code and the sequential number. The report code identifies the issuing organization, a specific program, or a type of document. The sequential number, which is assigned in sequence by each report issuing entity, is not included in this publication. Part I of this compilation is alphabetized by report codes followed by issuing installations. Part II lists the issuing organization followed by the assigned report code(s). In both Parts I and II, the names of issuing organizations appear for the most part in the form used at the time the reports were issued. However, for some of the more prolific installations which have had name changes, all entries have been merged under the current name.

Report number codes

International Nuclear Information System (INIS)

Nelson, R.N.

1985-05-01

This publication lists all report number codes processed by the Office of Scientific and Technical Information. The report codes are substantially based on the American National Standards Institute, Standard Technical Report Number (STRN)-Format and Creation Z39.23-1983. The Standard Technical Report Number (STRN) provides one of the primary methods of identifying a specific technical report. The STRN consists of two parts: The report code and the sequential number. The report code identifies the issuing organization, a specific program, or a type of document. The sequential number, which is assigned in sequence by each report issuing entity, is not included in this publication. Part I of this compilation is alphabetized by report codes followed by issuing installations. Part II lists the issuing organization followed by the assigned report code(s). In both Parts I and II, the names of issuing organizations appear for the most part in the form used at the time the reports were issued. However, for some of the more prolific installations which have had name changes, all entries have been merged under the current name

Building Numbers from Primes

Science.gov (United States)

Burkhart, Jerry

2009-01-01

Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…

Asymptotic numbers: Pt.1

International Nuclear Information System (INIS)

Todorov, T.D.

1980-01-01

The set of asymptotic numbers A as a system of generalized numbers including the system of real numbers R, as well as infinitely small (infinitesimals) and infinitely large numbers, is introduced. The detailed algebraic properties of A, which are unusual as compared with the known algebraic structures, are studied. It is proved that the set of asymptotic numbers A cannot be isomorphically embedded as a subspace in any group, ring or field, but some particular subsets of asymptotic numbers are shown to be groups, rings, and fields. The algebraic operation, additive and multiplicative forms, and the algebraic properties are constructed in an appropriate way. It is shown that the asymptotic numbers give rise to a new type of generalized functions quite analogous to the distributions of Schwartz allowing, however, the operation multiplication. A possible application of these functions to quantum theory is discussed

Rotation and Radiation Effects on MHD Flow through Porous Medium Past a Vertical Plate with Heat and Mass Transfer

Directory of Open Access Journals (Sweden)

Uday Singh Rajput

2017-11-01

Full Text Available Effects of rotation and radiation on unsteady MHD flow past a vertical plate with variable wall temperature and mass diffusion in the presence of Hall current is studied here. Earlier we studied chemical reaction effect on unsteady MHD flow past an exponentially accelerated inclined plate with variable temperature and mass diffusion in the presence of Hall current. We had obtained the results which were in agreement with the desired flow phenomenon. To study further, we are changing the model by considering radiation effect on fluid, and changing the geometry of the model. Here in this paper we are taking the plate positioned vertically upward and rotating with velocity Ω . Further, medium of the flow is taken as porous. The plate temperature and the concentration level near the plate increase linearly with time. The governing system of partial differential equations is transformed to dimensionless equations using dimensionless variables. The dimensionless equations under consideration have been solved by Laplace transform technique. The model contains equations of motion, diffusion equation and equation of energy. To analyze the solution of the model, desirable sets of the values of the parameters have been considered. The governing equations involved in the flow model are solved by the Laplace-transform technique. The results obtained have been analyzed with the help of graphs drawn for different parameters. The numerical values obtained for the drag at boundary and Nusselt number have been tabulated. We found that the values obtained for velocity, concentration and temperature are in concurrence with the actual flow of the fluid

Introduction to number theory

CERN Document Server

Vazzana, Anthony; Garth, David

2007-01-01

One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topics.

Intuitive numbers guide decisions

Directory of Open Access Journals (Sweden)

Ellen Peters

2008-12-01

Full Text Available Measuring reaction times to number comparisons is thought to reveal a processing stage in elementary numerical cognition linked to internal, imprecise representations of number magnitudes. These intuitive representations of the mental number line have been demonstrated across species and human development but have been little explored in decision making. This paper develops and tests hypotheses about the influence of such evolutionarily ancient, intuitive numbers on human decisions. We demonstrate that individuals with more precise mental-number-line representations are higher in numeracy (number skills consistent with previous research with children. Individuals with more precise representations (compared to those with less precise representations also were more likely to choose larger, later amounts over smaller, immediate amounts, particularly with a larger proportional difference between the two monetary outcomes. In addition, they were more likely to choose an option with a larger proportional but smaller absolute difference compared to those with less precise representations. These results are consistent with intuitive number representations underlying: a perceived differences between numbers, b the extent to which proportional differences are weighed in decisions, and, ultimately, c the valuation of decision options. Human decision processes involving numbers important to health and financial matters may be rooted in elementary, biological processes shared with other species.

Of colored numbers and numbered colors: interactive processes in grapheme-color synesthesia.

Science.gov (United States)

Gebuis, Titia; Nijboer, Tanja C W; van der Smagt, Maarten J

2009-01-01

Grapheme-color synesthetes experience a specific color when they see a grapheme but they do not report to perceive a grapheme when a color is presented. In this study, we investigate whether color can still evoke number-processes even when a vivid number experience is absent. We used color-number and number-color priming, both revealing faster responses in congruent compared to incongruent conditions. Interestingly, the congruency effect was of similar magnitude for both conditions, and a numerical distance effect was present only in the color-number priming task. In addition, a priming task in which synesthetes had to judge the parity of a colored number revealed faster responses in parity congruent than in parity incongruent trials. These combined results demonstrate that synesthesia is indeed bi-directional and of similar strength in both directions. Furthermore, they illustrate the precise nature of these interactions and show that the direction of these interactions is determined by task demands, not by the more vividly experienced aspect of the stimulus.

Alternative analysis: the prime numbers theory and an extension of the real numbers set

OpenAIRE

Sukhotin A.; Zvyagin M.

2016-01-01

Here we consider the theory of prime numbers at a new methodology. The theory of prime numbers is one of the most ancient mathematical branches. We found an estimate of the all prime numbers sum using the notions of infinite lager numbers and infinitely small numbers, farther we estimated the value of the maximal prime number. We proved that Hardy–Littlewood Hypothesis has the positive decision too. The infinite small numbers define a new methodology of the well–known function o(x) applicatio...

Charnock's Roughness Length Model and Non-dimensional Wind Profiles Over the Sea

DEFF Research Database (Denmark)

Pena Diaz, Alfredo; Gryning, Sven-Erik

2008-01-01

An analysis tool for the study of wind speed profiles over the water has been developed. The profiles are analysed using a modified dimensionless wind speed and dimensionless height, assuming that the sea surface roughness can be predicted by Charnock's roughness length model. In this form, the r...

Pumping Capacity of Pitched Blade Impellers in a Tall Vessel with a Draught Tube

Directory of Open Access Journals (Sweden)

J. Brož

2004-01-01

Full Text Available A study was made of the pumping capacity of pitched blade impellers (two, three, four, five and six blade pitched blade impellers with pitch angles α = 35° and 45° coaxially located in a cylindrical pilot plant vessel with cylindrical draught tube provided with a standard dished bottom. The draught tube was equipped with four equally spaced radial baffles above the impeller pumping liquid upwards towards the liquid surface. In all investigated cases the liquid aspect ratio H/T = 1.2 - 1.5, the draught tube / vessel diameter ratios DT /T = 0.2 and 0.4 and the impeller / draught tube diameter ratio D/DT = 0.875. The pumping capacity of the impeller was calculated from the radial profile of the axial component of the mean velocity in the draught tube below the impeller at such an axial distance from the impeller that the rotor does not affect the vorticity of the flow. The mean velocity was measured using a laser Doppler anemometer with forward scatter mode in a transparent draught tube and a transparent vessel of diameter T = 400 mm. Two series of experiments were performed, both of them under a turbulent regime of flow of the agitated liquid. First, the optimum height of the dished bottom was sought, and then the dependences of the dimensionless flow rate criterion and the impeller power number on the number of impeller blades were determined for both pitch angles tested under conditions of optimum ratio HT /DT. It follows from the results of the experiments that the optimum ratio HT /DT = 0.25 when the cross sectional areas of the horizontal flow around the bottom and the vertical inflow to the draught tube are the same. For all the tested pitched blade impellers the impeller power number when α = 45° exceeds the value of this quantity when pitch angle α  =   35°, while the flow rate number when α = 35° exceeds this quantity when α = 45°. On the other hand, the absolute values of the impeller power number when the draught tube was

Advanced number theory

CERN Document Server

Cohn, Harvey

1980-01-01

""A very stimulating book ... in a class by itself."" - American Mathematical MonthlyAdvanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject.The book is divided into three parts

Algebraic number theory

CERN Document Server

Weiss, Edwin

1998-01-01

Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis).Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract te

Numbers and brains.

Science.gov (United States)

Gallistel, C R

2017-12-01

The representation of discrete and continuous quantities appears to be ancient and pervasive in animal brains. Because numbers are the natural carriers of these representations, we may discover that in brains, it's numbers all the way down.

Small numbers are sensed directly, high numbers constructed from size and density.

Science.gov (United States)

Zimmermann, Eckart

2018-04-01

Two theories compete to explain how we estimate the numerosity of visual object sets. The first suggests that the apparent numerosity is derived from an analysis of more low-level features like size and density of the set. The second theory suggests that numbers are sensed directly. Consistent with the latter claim is the existence of neurons in parietal cortex which are specialized for processing the numerosity of elements in the visual scene. However, recent evidence suggests that only low numbers can be sensed directly whereas the perception of high numbers is supported by the analysis of low-level features. Processing of low and high numbers, being located at different levels of the neural hierarchy should involve different receptive field sizes. Here, I tested this idea with visual adaptation. I measured the spatial spread of number adaptation for low and high numerosities. A focused adaptation spread of high numerosities suggested the involvement of early neural levels where receptive fields are comparably small and the broad spread for low numerosities was consistent with processing of number neurons which have larger receptive fields. These results provide evidence for the claim that different mechanism exist generating the perception of visual numerosity. Whereas low numbers are sensed directly as a primary visual attribute, the estimation of high numbers however likely depends on the area size over which the objects are spread. Copyright © 2017 Elsevier B.V. All rights reserved.

Number projection method

International Nuclear Information System (INIS)

Kaneko, K.

1987-01-01

A relationship between the number projection and the shell model methods is investigated in the case of a single-j shell. We can find a one-to-one correspondence between the number projected and the shell model states

Elementary number theory

CERN Document Server

Dudley, Underwood

2008-01-01

Ideal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems-some computational and some classical, many original, and some with complete solutions. The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamenta

Investigation on the Flow in a Rotor-Stator Cavity with Centripetal Through-Flow

Directory of Open Access Journals (Sweden)

Bo Hu

2017-10-01

Full Text Available Daily and Nece distinguished four flow regimes in an enclosed rotor-stator cavity, which are dependent on the circumferential Reynolds number and dimensionless axial gap width. A diagram of the different flow regimes including the respective mean profiles for both tangential and radial velocity was developed. The coefficients for the different flow regimes have also been correlated. In centrifugal pumps and turbines, the centripetal through-flow is quite common from the outer radius of the impeller to the impeller eye, which has a strong influence on the radial pressure distribution, axial thrust and frictional torque. The influence of the centripetal through-flow on the cavity flow with different circumferential Reynolds numbers and dimensionless axial gap width is not sufficiently investigated. It is also quite important to convert the 2D Daily and Nece diagram into 3D by introducing the through-flow coefficient. In order to investigate the impact of the centripetal through-flow, a test rig is designed and built up at the University of Duisburg-Essen. The design of the test rig is described. The impact of the above mentioned parameters on the velocity profile, pressure distribution, axial thrust and frictional torque are presented and analyzed in this paper. The 3D Daily and Nece diagram introducing the through-flow coefficient is also organized in this paper.

Experimental and numerical investigation of reactive shock-accelerated flows

Energy Technology Data Exchange (ETDEWEB)

Bonazza, Riccardo [Univ. of Wisconsin, Madison, WI (United States). Dept. of Engineering Physics

2016-12-20

The main goal of this program was to establish a qualitative and quantitative connection, based on the appropriate dimensionless parameters and scaling laws, between shock-induced distortion of astrophysical plasma density clumps and their earthbound analog in a shock tube. These objectives were pursued by carrying out laboratory experiments and numerical simulations to study the evolution of two gas bubbles accelerated by planar shock waves and compare the results to available astrophysical observations. The experiments were carried out in an vertical, downward-firing shock tube, 9.2 m long, with square internal cross section (25×25 cm²). Specific goals were to quantify the effect of the shock strength (Mach number, M) and the density contrast between the bubble gas and its surroundings (usually quantified by the Atwood number, i.e. the dimensionless density difference between the two gases) upon some of the most important flow features (e.g. macroscopic properties; turbulence and mixing rates). The computational component of the work performed through this program was aimed at (a) studying the physics of multi-phase compressible flows in the context of astrophysics plasmas and (b) providing a computational connection between laboratory experiments and the astrophysical application of shock-bubble interactions. Throughout the study, we used the FLASH4.2 code to run hydrodynamical and magnetohydrodynamical simulations of shock bubble interactions on an adaptive mesh.

Experimental and numerical investigation of reactive shock-accelerated flows

International Nuclear Information System (INIS)

Bonazza, Riccardo

2016-01-01

The main goal of this program was to establish a qualitative and quantitative connection, based on the appropriate dimensionless parameters and scaling laws, between shock-induced distortion of astrophysical plasma density clumps and their earthbound analog in a shock tube. These objectives were pursued by carrying out laboratory experiments and numerical simulations to study the evolution of two gas bubbles accelerated by planar shock waves and compare the results to available astrophysical observations. The experiments were carried out in an vertical, downward-firing shock tube, 9.2 m long, with square internal cross section (25x25 cm"2). Specific goals were to quantify the effect of the shock strength (Mach number, M) and the density contrast between the bubble gas and its surroundings (usually quantified by the Atwood number, i.e. the dimensionless density difference between the two gases) upon some of the most important flow features (e.g. macroscopic properties; turbulence and mixing rates). The computational component of the work performed through this program was aimed at (a) studying the physics of multi-phase compressible flows in the context of astrophysics plasmas and (b) providing a computational connection between laboratory experiments and the astrophysical application of shock-bubble interactions. Throughout the study, we used the FLASH4.2 code to run hydrodynamical and magnetohydrodynamical simulations of shock bubble interactions on an adaptive mesh.

Unsteady magnetohydrodynamic thermal and diffusion boundary layer from a horizontal circular cylinder

Directory of Open Access Journals (Sweden)

Boričić Aleksandar Z.

2016-01-01

Full Text Available The unsteady 2-D dynamic, thermal, and diffusion magnetohydrodynamic laminar boundary layer flow over a horizontal cylinder of incompressible and electrical conductivity fluid, in mixed convection in the presence of heat source or sink and chemical reactions. The present magnetic field is homogenous and perpendicular to the body surface. It is assumed that induction of outer magnetic field is a function of longitudinal co-ordinate outer electric field is neglected and magnetic Reynolds number is significantly lower than one, i. e. considered the problem is in approximation without induction. Fluid electrical conductivity is constant. Free stream velocity, temperature, and concentration on the body are functions of longitudinal co-ordinate. The developed governing boundary layer equations and associated boundary conditions are made dimensionless using a suitable similarity transformation and similarity parameters. System of non-dimensionless equations is solved using the implicit finite difference three-diagonal and iteration method. Numerical results are obtained and presented for different Prandtl, Eckart, and Schmidt numbers, and values: magnetic parameter, temperature, and diffusion parameters, buoyancy temperature parameters, thermal parameter, and chemical reaction parameter. Variation of velocity profiles, temperature and diffusion distributions, and many integral and differential characteristics, boundary layer, are evaluated numerically for different values of the magnetic field. Transient effects of velocity, temperature and diffusion are analyzed. A part of obtained results is given in the form of figures and corresponding conclusions.

Numerical solutions for magnetohydrodynamic flow of nanofluid over a bidirectional non-linear stretching surface with prescribed surface heat flux boundary

Energy Technology Data Exchange (ETDEWEB)

Mahanthesh, B., E-mail: bmanths@gmail.com [Department of Mathematics, AIMS Institutes, Peenya, 560058 Bangalore (India); Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451 Shimoga, Karnataka (India); Gireesha, B.J., E-mail: bjgireesu@rediffmail.com [Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, 577451 Shimoga, Karnataka (India); Department of Mechanical Engineering, Cleveland State University, Cleveland, OH (United States); Gorla, R.S. Reddy, E-mail: r.gorla@csuohio.edu [Department of Mechanical Engineering, Cleveland State University, Cleveland, OH (United States); Abbasi, F.M., E-mail: abbasisarkar@gmail.com [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Shehzad, S.A., E-mail: ali_qau70@yahoo.com [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)

2016-11-01

Numerical solutions of three-dimensional flow over a non-linear stretching surface are developed in this article. An electrically conducting flow of viscous nanoliquid is considered. Heat transfer phenomenon is accounted under thermal radiation, Joule heating and viscous dissipation effects. We considered the variable heat flux condition at the surface of sheet. The governing mathematical equations are reduced to nonlinear ordinary differential systems through suitable dimensionless variables. A well-known shooting technique is implemented to obtain the results of dimensionless velocities and temperature. The obtained results are plotted for multiple values of pertinent parameters to discuss the salient features of these parameters on fluid velocity and temperature. The expressions of skin-friction coefficient and Nusselt number are computed and analyzed comprehensively through numerical values. A comparison of present results with the previous results in absence of nanoparticle volume fraction, mixed convection and magnetic field is computed and an excellent agreement noticed. We also computed the results for both linear and non-linear stretching sheet cases. - Highlights: • Hydromagnetic flow of nanofluid over a bidirectional non-linear stretching surface is examined. • Cu, Al{sub 2}O3 and TiO{sub 2} types nanoparticles are taken into account. • Numerical solutions have been computed and addressed. • The values of skin-friction and Nusselt number are presented.

Invitation to number theory

CERN Document Server

Ore, Oystein

2017-01-01

Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, … and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more. In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.

Experimental simulation of fragmentation and stratification of core debris on the core catcher of a fast breeder reactor

Energy Technology Data Exchange (ETDEWEB)

Pillai, Dipin S.; Vignesh, R. [Indian Institute of Technology, Chennai, Tamil Nadu (India); Sudha, A. Jasmin, E-mail: jasmin@igcar.gov.in [Safety Engineering Division, Reactor Design Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, Tamil Nadu (India); Pushpavanam, S.; Sundararajan, T. [Indian Institute of Technology, Chennai, Tamil Nadu (India); Nashine, B.K.; Selvaraj, P. [Safety Engineering Division, Reactor Design Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, Tamil Nadu (India)

2016-05-15

Highlights: • Fragmentation of two simultaneous metals jets in a bulk coolant analysed. • Particle size from experiments compared with theoretical analysis. • Jet breakup modes explained using dimensionless numbers. • Settling aspects of aluminium and lead debris on collector plate studied. • Results analysed in light of core debris settling on core catcher in a FBR. - Abstract: The complex and coupled phenomena of two simultaneous molten metal jets fragmenting inside a quiescent liquid pool and settling on a collector plate are experimentally analysed in the context of safety analysis of a fast breeder reactor (FBR) in the post accident heat removal phase. Following a hypothetical core melt down accident in a FBR, a major portion of molten nuclear fuel and clad/structural material which are collectively termed as ‘corium’ undergoes fragmentation in the bulk coolant sodium in the lower plenum of the reactor main vessel and settles on the core catcher plate. The coolability of this decay heat generating debris bed is dependent on the particle size distribution and its layering i.e., stratification. Experiments have been conducted with two immiscible molten metals of different densities poured inside a coolant medium to understand their fragmentation behaviour and to assess the possibility of formation of a stratified debris bed. Molten aluminium and lead have been used as simulants in place of molten stainless steel and nuclear fuel to facilitate easy handling. This paper summarizes the major findings from these experiments. The fragmentation of the two molten metals are explained in the light of relevant dimensionless numbers such as Reynolds number and Weber Number. The mass median diameter of the fragmented debris is predicted from nonlinear stability analysis of slender jets for lead jet and using Rayleigh's classical theory of jet breakup for aluminium jet. The agreement of the predicted values with the experimental results is good. These

The distribution of prime numbers and associated problems in number theory

International Nuclear Information System (INIS)

Nair, M.

1991-01-01

Some problems in number theory, namely the gaps between consecutive primes, the distribution of primes in arithmetic progressions, Brun-Titchmarsh theorem, Fermat's last theorem, The Thue equation, the gaps between square-free numbers are discussed

Funny Numbers

Directory of Open Access Journals (Sweden)

Theodore M. Porter

2012-12-01

Full Text Available The struggle over cure rate measures in nineteenth-century asylums provides an exemplary instance of how, when used for official assessments of institutions, these numbers become sites of contestation. The evasion of goals and corruption of measures tends to make these numbers “funny” in the sense of becoming dis-honest, while the mismatch between boring, technical appearances and cunning backstage manipulations supplies dark humor. The dangers are evident in recent efforts to decentralize the functions of governments and corporations using incen-tives based on quantified targets.

Number-unconstrained quantum sensing

Science.gov (United States)

Mitchell, Morgan W.

2017-12-01

Quantum sensing is commonly described as a constrained optimization problem: maximize the information gained about an unknown quantity using a limited number of particles. Important sensors including gravitational wave interferometers and some atomic sensors do not appear to fit this description, because there is no external constraint on particle number. Here, we develop the theory of particle-number-unconstrained quantum sensing, and describe how optimal particle numbers emerge from the competition of particle-environment and particle-particle interactions. We apply the theory to optical probing of an atomic medium modeled as a resonant, saturable absorber, and observe the emergence of well-defined finite optima without external constraints. The results contradict some expectations from number-constrained quantum sensing and show that probing with squeezed beams can give a large sensitivity advantage over classical strategies when each is optimized for particle number.

Study of flow past an exponentially accelerated isothermal vertical plate in the presence of chemical reaction

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2010-01-01

Full Text Available Theoretical study of unsteady flow past an exponentially accelerated infinite isothermal vertical plate with variable mass diffusion has been presented in the presence of homogeneous chemical reaction of first order. The plate temperature is raised to Tw and species concentration level near the plate is made to rise linearly with time. The dimensionless governing equations are solved using Laplace-transform technique. The velocity profiles are studied for different physical parameters like chemical reaction parameter, thermal Grashof number, mass Grashof number, a and time. It is observed that the velocity increases with increasing values of a or t. But the trend is just reversed with respect to K.

Grammatical typology and frequency analysis: number availability and number use

Directory of Open Access Journals (Sweden)

Dunstan Brown

2013-12-01

Full Text Available The Smith-Stark hierarchy, a version of the Animacy Hierarchy, offers a typology of the cross-linguistic availability of number. The hierarchy predicts that the availability of number is not arbitrary. For any language, if the expression of plural is available to a noun, it is available to any noun of a semantic category further to the left of the hierarchy. In this article we move one step further by showing that the structure of the hierarchy can be observed in a statistical model of number use in Russian. We also investigate three co-variates: plural preference, pluralia tantum and irregularity effects; these account for an item's behaviour being different than that solely expected from its animacy position.

Numbers and computers

CERN Document Server

Kneusel, Ronald T

2015-01-01

This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers. Divided into two parts, the first deals with standard representations of integers and floating point numb

Heat transfer effects on flow past an exponentially accelerated vertical plate with variable temperature

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2008-01-01

Full Text Available An exact solution to the problem of flow past an exponentially accelerated infinite vertical plate with variable temperature is analyzed. The temperature of the plate is raised linearly with time t. The dimensionless governing equations are solved using Laplace-transform technique. The velocity and temperature profiles are studied for different physical parameters like thermal Grashof number Gr, time and an accelerating parameter a. It is observed that the velocity increases with increasing values of a or Gr.

Model Experiments for the Determination of Airflow in Large Spaces

DEFF Research Database (Denmark)

Nielsen, Peter V.

Model experiments are one of the methods used for the determination of airflow in large spaces. This paper will discuss the formation of the governing dimensionless numbers. It is shown that experiments with a reduced scale often will necessitate a fully developed turbulence level of the flow....... Details of the flow from supply openings are very important for the determination of room air distribution. It is in some cases possible to make a simplified supply opening for the model experiment....

Really big numbers

CERN Document Server

Schwartz, Richard Evan

2014-01-01

In the American Mathematical Society's first-ever book for kids (and kids at heart), mathematician and author Richard Evan Schwartz leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system. By means of engaging, imaginative visuals and endearing narration, Schwartz manages the monumental task of presenting the complex concept of Big Numbers in fresh and relatable ways. The book begins with small, easily observable numbers before building up to truly gigantic ones, like a nonillion, a tredecillion, a googol, and even ones too huge for names! Any person, regardless of age, can benefit from reading this book. Readers will find themselves returning to its pages for a very long time, perpetually learning from and growing with the narrative as their knowledge deepens. Really Big Numbers is a wonderful enrichment for any math education program and is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual i...

Templates, Numbers & Watercolors.

Science.gov (United States)

Clemesha, David J.

1990-01-01

Describes how a second-grade class used large templates to draw and paint five-digit numbers. The lesson integrated artistic knowledge and vocabulary with their mathematics lesson in place value. Students learned how draftspeople use templates, and they studied number paintings by Charles Demuth and Jasper Johns. (KM)

Radiation effects on the mixed convection flow induced by an inclined stretching cylinder with non-uniform heat source/sink.

Science.gov (United States)

Hayat, Tasawar; Qayyum, Sajid; Alsaedi, Ahmed; Asghar, Saleem

2017-01-01

This study investigates the mixed convection flow of Jeffrey liquid by an impermeable inclined stretching cylinder. Thermal radiation and non-uniform heat source/sink are considered. The convective boundary conditions at surface are imposed. Nonlinear expressions of momentum, energy and concentration are transformed into dimensionless systems. Convergent homotopic solutions of the governing systems are worked out by employing homotopic procedure. Impact of physical variables on the velocity, temperature and concentration distributions are sketched and discussed. Numerical computations for skin friction coefficient, local Nusselt and Sherwood numbers are carried out. It is concluded that velocity field enhances for Deborah number while reverse situation is observed regarding ratio of relaxation to retardation times. Temperature and heat transfer rate are enhanced via larger thermal Biot number. Effect of Schmidt number on the concentration and local Sherwood number is quite reverse.

The Brothel Phone Number

DEFF Research Database (Denmark)

Korsby, Trine Mygind

2017-01-01

Taking a point of departure in negotiations for access to a phone number for a brothel abroad, the article demonstrates how a group of pimps in Eastern Romania attempt to extend their local business into the rest of the EU. The article shows how the phone number works as a micro-infrastructure in......Taking a point of departure in negotiations for access to a phone number for a brothel abroad, the article demonstrates how a group of pimps in Eastern Romania attempt to extend their local business into the rest of the EU. The article shows how the phone number works as a micro...... in turn cultivate and maximize uncertainty about themselves in others. When making the move to go abroad into unknown terrains, accessing the infrastructure generated by the phone number can provide certainty and consolidate one’s position within criminal networks abroad. However, at the same time......, mishandling the phone number can be dangerous and in that sense produce new doubts and uncertainties....

Random number generation

International Nuclear Information System (INIS)

Coveyou, R.R.

1974-01-01

The subject of random number generation is currently controversial. Differing opinions on this subject seem to stem from implicit or explicit differences in philosophy; in particular, from differing ideas concerning the role of probability in the real world of physical processes, electronic computers, and Monte Carlo calculations. An attempt is made here to reconcile these views. The role of stochastic ideas in mathematical models is discussed. In illustration of these ideas, a mathematical model of the use of random number generators in Monte Carlo calculations is constructed. This model is used to set up criteria for the comparison and evaluation of random number generators. (U.S.)

On the number of special numbers

Indian Academy of Sciences (India)

We now apply the theory of the Thue equation to obtain an effective bound on m. Indeed, by Lemma 3.2, we can write m2 = ba3 and m2 − 4 = cd3 with b, c cubefree. By the above, both b, c are bounded since they are cubefree and all their prime factors are less than e63727. Now we have a finite number of. Thue equations:.

Qualitative internal surface roughness classification using acoustic emission

International Nuclear Information System (INIS)

Mohd Hafizi Zohari; Mohd Hanif Saad

2009-04-01

This paper describes a novel new nondestructive method of qualitative internal surface roughness classification for pipes utilizing Acoustic Emission (AE) signal. Two different flowrate are introduced in a pipe obstructed using normally available components (e.g.: valve). The AE signal at suitable location from the obstruction are obtained and the peak amplitudes, RMS amplitude and energy of the AE signal are obtained. A dimensionless number, the Bangi Number, AB, is then calculated as a ratio of the AE parameters (peak amplitude, RMS amplitude or energy) in low flowrate measurement compared to the AE parameters in high flowrate measurement. It was observed that the Bangi Number, AB obtained can then be used to successfully discriminate between rough and smooth internal surface roughness. (author)

Bernoulli numbers and zeta functions

CERN Document Server

Arakawa, Tsuneo; Kaneko, Masanobu

2014-01-01

Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen–von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler–Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of ...

α φ µ π ψ

African Journals Online (AJOL)

ADOWIE PERE

Volumetric flow rate, STB/D r. Radius, ft. D r. Dimensionless radius e r. External radius, ft. eD r. Dimensionless external radius w ... wellbore using the finite element method. Theory: The law of conservation of mass, Darcy's law and the equation of state has been combined to obtain the following partial differential equation:.

Analysis of graphite gasification by water vapor at different conversions

International Nuclear Information System (INIS)

Xiaowei, Luo; Xiaoyu, Yu; Suyuan, Yu; Jean-Charles, Robin

2014-01-01

Highlights: • Graphite was gasified at different conversions. • The reaction temperature influences on the dimensionless the reaction rate. • The thickness or radius influence on the dimensionless reaction rate. - Abstract: The gasification rate of porous solids varies with the conversions with the rate increasing to a maximum and then decreasing. Many graphite gasification experiments have illustrated that the maximum gasification rates occur at different conversions for different temperatures and sample geometries. Thus, the gasification rate is related to the conversion, temperature and geometry of the graphite. The influences of those factors were studied for the graphite gasification by water vapor. A theoretical analysis was done on the basis of several logical assumptions. The influence of temperatures on the reaction rate was investigated for plate-like and cylindrical graphite. The effects of thickness for a plate-like graphite sample and of radius for a cylindrical sample on the reaction rate were also studied theoretically. The results reveal that the maximum dimensionless reaction rate decreases with reaction temperature. The plate thickness or the cylinder radius also affects the maximum dimensionless reaction rate

Similarity rules of thermal stratification phenomena for water and sodium

International Nuclear Information System (INIS)

Ohtsuka, M.; Ikeda, T.; Yamakawa, M.; Shibata, Y.; Moriya, S.; Ushijima, S.; Fujimoto, K.

1988-01-01

Similarity rules for thermal stratification phenomena were studied using sodium and water experiments with scaled cylindrical vessels. The vessel dimensions were identical to focus on the effect of differences in fluid properties upon the phenomena. Comparisons of test results between sodium and water elucidated similar and dissimilar characteristics for thermal stratification phenomena which appeared in the scaled vessels. Results were as follows: (1) The dimensionless upward velocity of the thermal stratification interface was proportional to Ri -0.74 for water and sodium during the period when the buoyancy effect was dominant. (2) Dimensionless temperature transient rate at the outlet slit decreased with Ri for sodium and remained constant for water where Ri>0.2. The applicability of the scaled test results to an actual power plant was also studied by using multi-dimensional numerical analysis which was verified by the water and sodium experiments. Water experiments could simulate liquid metal fast breeder reactor flows more accurately than sodium experiments for dimensionless temperature gradient at the thermal stratification interface and dimensionless temperature transient rate at the intermediate heat exchanger inlet

Transcendental numbers

CERN Document Server

Murty, M Ram

2014-01-01

This book provides an introduction to the topic of transcendental numbers for upper-level undergraduate and graduate students. The text is constructed to support a full course on the subject, including descriptions of both relevant theorems and their applications. While the first part of the book focuses on introducing key concepts, the second part presents more complex material, including applications of Baker’s theorem, Schanuel’s conjecture, and Schneider’s theorem. These later chapters may be of interest to researchers interested in examining the relationship between transcendence and L-functions. Readers of this text should possess basic knowledge of complex analysis and elementary algebraic number theory.

Dynamics of viscoelastic fluid filaments in microfluidic devices

Science.gov (United States)

Steinhaus, Benjamin; Shen, Amy Q.; Sureshkumar, Radhakrishna

2007-07-01

The effects of fluid elasticity and channel dimension on polymeric droplet formation in the presence of a flowing continuous Newtonian phase are investigated systematically by using different molecular weight (MW) poly(ethylene oxide) (PEO) solutions and varying microchannel dimensions with constant orifice width (w) to depth (h) ratio (w/h=1/2) and w =25μm, 50μm, 100μm, and 1mm. The flow rate is varied so that the mean shear rate is practically identical for all cases considered. Relevant times scales include inertia-capillary Rayleigh time τR=(Rmax3ρ/σ)1/2, viscocapillary Tomotika time τT=η0Rmax/σ, and the polymer relaxation time λ, where ρ is the fluid density of the dispersed phase, σ is the interfacial tension, η0 is the zero shear viscosity of the dispersed polymer phase, and Rmax is the maximum filament radius. Dimensionless numbers include the elasticity number E =λν/Rmax2, elastocapillary number Ec=λ/τT, and Deborah number, De =λ/τR, where ν =η0/ρ is the kinematic shear viscosity of the fluids. Experiments show that higher MW Boger fluids possessing longer relaxation times and larger extensional viscosities exhibit longer thread lengths and longer pinch-off times (tp). The polymer filament dynamics are controlled primarily by an elastocapillary mechanism with increasing elasticity effect at smaller length scales (larger E and Ec). However, with weaker elastic effects (i.e., larger w and lower MW), pinch-off is initiated by inertia-capillary mechanisms, followed by an elastocapillary regime. A high degree of correlation exists between the dimensionless pinch-off times and the elasticity numbers. We also observe that higher elasticity number E yields smaller effective λ. Based on the estimates of polymer scission probabilities predicted by Brownian dynamics simulations for uniaxial extensional flows, polymer chain scission is likely to occur for ultrasmall orifices and high MW fluids, yielding smaller λ. Finally, the inhibition of

Symmetry mappings concomitant to particle-number-conservation-baryon-number conservation

International Nuclear Information System (INIS)

Davis, W.R.

1977-01-01

Four theorem serve to demonstrate that matter fields in space-time admit certain timelike symmetry mappings concomitant to the familiar notion of particle number conservation, which can be more fundamentally accounted for by a type of projective invariance principle. These particular symmetry mappings include a family of symmetry properties that may be admitted by Riemannian space-times. In their strongest form, the results obtained provide some insight relating to the conservation of baryon number

A closed form solution for the response of a long elastic beam to dynamic loading

International Nuclear Information System (INIS)

Mittal, R.K.

1989-01-01

Closed form solutions have been obtained using Fourier transform method for the deflection, curvature and particle velocity of a long elastic beam when it is subjected to a concentrated transverse force which is varying with time. These solutions have been illustrated with the help of two force histories, i.e. a half-sine pulse and a rectangular pulse. Dimensionless parameters representing deflection, curvature and particle velocity have been plotted as functions of dimensionless distance and dimensionless time. Furthermore, the particular case of constant velocity impact which has been studied by other authors using different techniques has also been considered in the present paper and the results compare within numerical errors involved in the evaluation of integrals. (orig.) [de

Scaling for Dynamical Systems in Biology.

Science.gov (United States)

Ledder, Glenn

2017-11-01

Asymptotic methods can greatly simplify the analysis of all but the simplest mathematical models and should therefore be commonplace in such biological areas as ecology and epidemiology. One essential difficulty that limits their use is that they can only be applied to a suitably scaled dimensionless version of the original dimensional model. Many books discuss nondimensionalization, but with little attention given to the problem of choosing the right scales and dimensionless parameters. In this paper, we illustrate the value of using asymptotics on a properly scaled dimensionless model, develop a set of guidelines that can be used to make good scaling choices, and offer advice for teaching these topics in differential equations or mathematical biology courses.

Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model

Science.gov (United States)

Cheviakov, Alexei F.

2018-05-01

A fully nonlinear model of Choi and Camassa (1999) describing one-dimensional incompressible dynamics of two non-mixing fluids in a horizontal channel, under a shallow water approximation, is considered. An equivalence transformation is presented, leading to a special dimensionless form of the system, involving a single dimensionless constant physical parameter, as opposed to five parameters present in the original model. A first-order dimensionless ordinary differential equation describing traveling wave solutions is analyzed. Several multi-parameter families of physically meaningful exact closed-form solutions of the two-fluid model are derived, corresponding to periodic, solitary, and kink-type bidirectional traveling waves; specific examples are given, and properties of the exact solutions are analyzed.

The effective thermal conductivity of porous media based on statistical self-similarity

International Nuclear Information System (INIS)

Kou Jianlong; Wu Fengmin; Lu Hangjun; Xu Yousheng; Song Fuquan

2009-01-01

A fractal model is presented based on the thermal-electrical analogy technique and statistical self-similarity of fractal saturated porous media. A dimensionless effective thermal conductivity of saturated fractal porous media is studied by the relationship between the dimensionless effective thermal conductivity and the geometrical parameters of porous media with no empirical constant. Through this study, it is shown that the dimensionless effective thermal conductivity decreases with the increase of porosity (φ) and pore area fractal dimension (D f ) when k s /k g >1. The opposite trends is observed when k s /k g t ). The model predictions are compared with existing experimental data and the results show that they are in good agreement with existing experimental data.

An Interpretation of the Laminar-Turbulent Transition Startup against the Consideration of the Transverse Viscosity Factor

Science.gov (United States)

Kolodezhnov, V. N.

2018-03-01

This paper proposes a rheological model of a fluid having the Newtonian model applicability limit and a potential for further “addition” of the transverse viscosity factor. The dynamic equations for a fluid that has such rheological model are discussed, the analysis of which demonstrates the possibility of “generating” the cross stream velocity components. The transition to the dimensionless notation introduces four dimensionless complexes of local characterization for the transition conditions in the neighborhood of the flow region point in question. Based on such dimensionless complexes and using the known experimental data, the empiric conditions of “generating” the cross stream velocity components and starting the laminar-turbulent transition are proposed.

Natural convection with evaporation in a vertical cylindrical cavity under the effect of temperature-dependent surface tension

Science.gov (United States)

Kozhevnikov, Danil A.; Sheremet, Mikhail A.

2018-01-01

The effect of surface tension on laminar natural convection in a vertical cylindrical cavity filled with a weak evaporating liquid has been analyzed numerically. The cylindrical enclosure is insulated at the bottom, heated by a constant heat flux from the side, and cooled by a non-uniform evaporative heat flux from the top free surface having temperature-dependent surface tension. Governing equations with corresponding boundary conditions formulated in dimensionless stream function, vorticity, and temperature have been solved by finite difference method of the second-order accuracy. The influence of Rayleigh number, Marangoni number, and aspect ratio on the liquid flow and heat transfer has been studied. Obtained results have revealed that the heat transfer rate at free surface decreases with Marangoni number and increases with Rayleigh number, while the average temperature inside the cavity has an opposite behavior; namely, it growths with Marangoni number and reduces with Rayleigh number.

The adventure of numbers

CERN Document Server

Godefroy, Gilles

2004-01-01

Numbers are fascinating. The fascination begins in childhood, when we first learn to count. It continues as we learn arithmetic, algebra, geometry, and so on. Eventually, we learn that numbers not only help us to measure the world, but also to understand it and, to some extent, to control it. In The Adventure of Numbers, Gilles Godefroy follows the thread of our expanding understanding of numbers to lead us through the history of mathematics. His goal is to share the joy of discovering and understanding this great adventure of the mind. The development of mathematics has been punctuated by a n

Numbers, sequences and series

CERN Document Server

Hirst, Keith

1994-01-01

Number and geometry are the foundations upon which mathematics has been built over some 3000 years. This book is concerned with the logical foundations of number systems from integers to complex numbers. The author has chosen to develop the ideas by illustrating the techniques used throughout mathematics rather than using a self-contained logical treatise. The idea of proof has been emphasised, as has the illustration of concepts from a graphical, numerical and algebraic point of view. Having laid the foundations of the number system, the author has then turned to the analysis of infinite proc

Optokinetic stimulation modulates neglect for the number space: Evidence from mental number interval bisection

Directory of Open Access Journals (Sweden)

Konstantinos ePriftis

2012-02-01

Full Text Available Behavioral, neuropsychological, and neuroimaging data support the idea that numbers are represented along a mental number line (MNL, an analogical, visuo-spatial representation of number magnitude. The MNL is left-to-right oriented, with small numbers on the left and larger numbers on the right. Left neglect patients are impaired in processing the left side of the MNL and show a rightward deviation in the mental bisection of numerical intervals. In the present study we investigated the effects of optokinetic stimulation (OKS -a technique inducing spatial attention shifts by means of activation of the optokinetic nystagmus- on mental number interval bisection. One patient with left neglect following right hemisphere stroke (BG and four control patients with right hemisphere damage, but without neglect, performed the mental number interval bisection task in three experimental conditions of OKS: static, leftward, and rightward. In the static condition, BG misbisected to the right of the true midpoint. BG misbisected to the left following leftward OKS, but again to the right of the midpoint following rightward OKS. In contrast, the performance of controls was not significantly affected by the direction of OKS. We argue that shifts of visuospatial attention, induced by OKS, may affect the mental number interval bisection, suggesting the presence of an interaction between the processing of number magnitude and the processing of the perceptual space, in patients with neglect for the mental number space.

Fermion number in supersymmetric models

International Nuclear Information System (INIS)

Mainland, G.B.; Tanaka, K.

1975-01-01

The two known methods for introducing a conserved fermion number into supersymmetric models are discussed. While the introduction of a conserved fermion number often requires that the Lagrangian be massless or that bosons carry fermion number, a model is discussed in which masses can be introduced via spontaneous symmetry breaking and fermion number is conserved at all stages without assigning fermion number to bosons. (U.S.)

Higher-order Nielsen numbers

Directory of Open Access Journals (Sweden)

Saveliev Peter

2005-01-01

Full Text Available Suppose , are manifolds, are maps. The well-known coincidence problem studies the coincidence set . The number is called the codimension of the problem. More general is the preimage problem. For a map and a submanifold of , it studies the preimage set , and the codimension is . In case of codimension , the classical Nielsen number is a lower estimate of the number of points in changing under homotopies of , and for an arbitrary codimension, of the number of components of . We extend this theory to take into account other topological characteristics of . The goal is to find a "lower estimate" of the bordism group of . The answer is the Nielsen group defined as follows. In the classical definition, the Nielsen equivalence of points of based on paths is replaced with an equivalence of singular submanifolds of based on bordisms. We let , then the Nielsen group of order is the part of preserved under homotopies of . The Nielsen number of order is the rank of this group (then . These numbers are new obstructions to removability of coincidences and preimages. Some examples and computations are provided.

Complex numbers in n dimensions

CERN Document Server

Olariu, Silviu

2002-01-01

Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined. The first type of hypercomplex numbers, called polar hypercomplex numbers, is characterized by the presence in an even number of dimensions greater or equal to 4 of two polar axes, and by the presence in an odd number of dimensions of one polar axis. The other type of hypercomplex numbers exists as a distinct entity only when the number of dimensions n of the space is even, and since the position of a point is specified with the aid of n/2-1 planar angles, these numbers have been called planar hypercomplex numbers. The development of the concept of analytic functions of hypercomplex variables was rendered possible by the existence of an exponential form of the n-complex numbe...

Optokinetic Stimulation Modulates Neglect for the Number Space: Evidence from Mental Number Interval Bisection

Science.gov (United States)

Priftis, Konstantinos; Pitteri, Marco; Meneghello, Francesca; Umiltà, Carlo; Zorzi, Marco

2012-01-01

Behavioral, neuropsychological, and neuroimaging data support the idea that numbers are represented along a mental number line (MNL), an analogical, visuospatial representation of number magnitude. The MNL is left-to-right oriented in Western cultures, with small numbers on the left and larger numbers on the right. Left neglect patients are impaired in the mental bisection of numerical intervals, with a bias toward larger numbers that are relatively to the right on the MNL. In the present study we investigated the effects of optokinetic stimulation (OKS) – a technique inducing visuospatial attention shifts by means of activation of the optokinetic nystagmus – on number interval bisection. One patient with left neglect following right-hemisphere stroke (BG) and four control patients with right-hemisphere damage, but without neglect, performed the number interval bisection task in three conditions of OKS: static, leftward, and rightward. In the static condition, BG misbisected to the right of the true midpoint. BG misbisected to the left following leftward OKS, and again to the right of the midpoint following rightward OKS. Moreover, the variability of BG’s performance was smaller following both leftward and rightward OKS, suggesting that the attentional bias induced by OKS reduced the “indifference zone” that is thought to underlie the length effect reported in bisection tasks. We argue that shifts of visuospatial attention, induced by OKS, may affect number interval bisection, thereby revealing an interaction between the processing of the perceptual space and the processing of the number space. PMID:22363280

Compendium of Experimental Cetane Numbers

Energy Technology Data Exchange (ETDEWEB)

Yanowitz, Janet [Ecoengineering, Sharonville, OH (United States); Ratcliff, Matthew A. [National Renewable Energy Lab. (NREL), Golden, CO (United States); McCormick, Robert L. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Taylor, J. D. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Murphy, M. J. [Battelle, Columbus, OH (United States)

2017-02-22

This report is an updated version of the 2014 Compendium of Experimental Cetane Number Data and presents a compilation of measured cetane numbers for pure chemical compounds. It includes all available single-compound cetane number data found in the scientific literature up until December 2016 as well as a number of previously unpublished values, most measured over the past decade at the National Renewable Energy Laboratory. This version of the compendium contains cetane values for 496 pure compounds, including 204 hydrocarbons and 292 oxygenates. 176 individual measurements are new to this version of the compendium, all of them collected using ASTM Method D6890, which utilizes an Ignition Quality Tester (IQT) a type of constant-volume combustion chamber. For many compounds, numerous measurements are included, often collected by different researchers using different methods. The text of this document is unchanged from the 2014 version, except for the numbers of compounds in Section 3.1, the Appendices, Table 1. Primary Cetane Number Data Sources and Table 2. Number of Measurements Included in Compendium. Cetane number is a relative ranking of a fuel's autoignition characteristics for use in compression ignition engines. It is based on the amount of time between fuel injection and ignition, also known as ignition delay. The cetane number is typically measured either in a single-cylinder engine or a constant-volume combustion chamber. Values in the previous compendium derived from octane numbers have been removed and replaced with a brief analysis of the correlation between cetane numbers and octane numbers. The discussion on the accuracy and precision of the most commonly used methods for measuring cetane number has been expanded, and the data have been annotated extensively to provide additional information that will help the reader judge the relative reliability of individual results.

Microsoft Support Phone Number +1-877-353-1149(toll-free) Microsoft Helpline Phone Number

OpenAIRE

Allina willson

2018-01-01

Microsoft Helpline Phone Number Call Now: +1-877-353-1149 for Microsoft support and services. This is Trusted Microsoft Support number provide instant support.if you get any problem while using Microsoft office just relaxed because Microsoft support phone number +1-877-353-1149 is here to provide instant help of microsoft issues. Just dial our Microsoft support phone number +1-877-353-1149 and get instant online support.

A Numbers Game

DEFF Research Database (Denmark)

Levin, Bruce R; McCall, Ingrid C.; Perrot, Veronique

2017-01-01

We postulate that the inhibition of growth and low rates of mortality of bacteria exposed to ribosome-binding antibiotics deemed bacteriostatic can be attributed almost uniquely to these drugs reducing the number of ribosomes contributing to protein synthesis, i.e., the number of effective......-targeting bacteriostatic antibiotics, the time before these bacteria start to grow again when the drugs are removed, referred to as the post-antibiotic effect (PAE), is markedly greater for constructs with fewer rrn operons than for those with more rrn operons. We interpret the results of these other experiments reported...... here as support for the hypothesis that the reduction in the effective number of ribosomes due to binding to these structures provides a sufficient explanation for the action of bacteriostatic antibiotics that target these structures....

Bell numbers, determinants and series

Indian Academy of Sciences (India)

In this article, we study Bell numbers and Uppuluri Carpenter numbers. We obtain various expressions and relations between them. These include polynomial recurrences and expressions as determinants of certain matrices of binomial coefficients. Keywords. p-adic series; Bell numbers. 1. Introduction. Bell numbers, Bn [2] ...

Dimensionless Energy Conversion Characteristics of an Air-Powered Hydraulic Vehicle

OpenAIRE

Dongkai Shen; Qilong Chen; Yixuan Wang

2018-01-01

Due to the advantages of resource conservation and less exhaust emissions, compressed air-powered vehicle has attracted more and more attention. To improve the power and efficiency of air-powered vehicle, an air-powered hydraulic vehicle was proposed. As the main part of the air-powered hydraulic vehicles, HP transformer (short for Hydropneumatic transformer) is used to convert the pneumatic power to higher hydraulic power. In this study, to illustrate the energy conversion characteristics of...

Finite element and network electrical simulation of rotating magnetofluid flow in nonlinear porous media with inclined magnetic field and hall currents

Directory of Open Access Journals (Sweden)

Bég Anwar O.

2014-01-01

Full Text Available A mathematical model is presented for viscous hydromagnetic flow through a hybrid non-Darcy porous media rotating generator. The system is simulated as steady, incompressible flow through a nonlinear porous regime intercalated between parallel plates of the generator in a rotating frame of reference in the presence of a strong, inclined magnetic field A pressure gradient term is included which is a function of the longitudinal coordinate. The general equations for rotating viscous magnetohydrodynamic flow are presented and neglecting convective acceleration effects, the two-dimensional viscous flow equations are derived incorporating current density components, porous media drag effects, Lorentz drag force components and Hall current effects. Using an appropriate group of dimensionless variables, the momentum equations for primary and secondary flow are rendered nondimensional and shown to be controlled by six physical parameters-Hartmann number (Ha, Hall current parameter (Nh, Darcy number (Da, Forchheimer number (Fs, Ekman number (Ek and dimensionless pressure gradient parameter (Np, in addition to one geometric parameter-the orientation of the applied magnetic field (θ . Several special cases are extracted from the general model, including the non-porous case studied earlier by Ghosh and Pop (2006. A numerical solution is presented to the nonlinear coupled ordinary differential equations using both the Network Simulation Method and Finite Element Method, achieving excellent agreement. Additionally very good agreement is also obtained with the earlier analytical solutions of Ghosh and Pop (2006. for selected Ha, Ek and Nh values. We examine in detail the effects of magnetic field, rotation, Hall current, bulk porous matrix drag, second order porous impedance, pressure gradient and magnetic field inclination on primary and secondary velocity distributions and also frictional shear stresses at the plates. Primary velocity is seen to decrease

Women in numbers Europe II contributions to number theory and arithmetic geometry

CERN Document Server

Ozman, Ekin; Johnson-Leung, Jennifer; Newton, Rachel

2018-01-01

Inspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects started at the conference, expository papers describing ongoing research, and contributed papers from women number theorists outside the conference make up this diverse volume. Topics cover a broad range of topics such as arithmetic dynamics, failure of local-global principles, geometry in positive characteristics, and heights of algebraic integers. The use of tools from algebra, analysis and geometry, as well as computational methods exemplifies the wealth of techniques available to modern researchers in number theory. Exploring connections between different branches of mathematics and combining different points of view, these papers continue the tradition of supporting and highlighting the contributions of women number theorists at a variety of career stages. Perfect for students and researche...

RELATIONSHIP BETWEEN MOBILE NUMBER PORTABILITY AND CONSUMER CHOICE OF ACTIVE MULTIPLE MOBILE PHONE NUMBERS IN GHANA

OpenAIRE

Solomon A. Keelson; Addo J. Odei

2014-01-01

The use of multiple mobile phone numbers in Ghana has become a dominate phenomenon in recent years. The introduction of mobile number portability (MNP) makes it possible for a subscriber to conveniently switch from one mobile network to another without losing his or her number. Because of mobile number portability, we expected that use of multiple numbers would become less attractive. This study examines how mobile number portability has affected the use of multiple phone numbers. We use top,...

Fixed-bed column studies of total organic carbon removal from industrial wastewater by use of diatomite decorated with polyethylenimine-functionalized pyroxene nanoparticles.

Science.gov (United States)

Hethnawi, Afif; Manasrah, Abdallah D; Vitale, Gerardo; Nassar, Nashaat N

2018-03-01

In this study, a fixed-bed column adsorption process was employed to remove organic pollutants from a real industrial wastewater effluent using polyethylenimine-functionalized pyroxene nanoparticles (PEI-PY) embedded into Diatomite at very low mass percentage. Various dynamic parameters (e.g., inlet concentration, inlet flow rate, bed height, and PEI-nanoparticle concentration in Diatomite, (%nps)) were investigated to determine the breakthrough behavior. The obtained breakthrough curves were fit with a convection-dispersion model to determine the characteristic parameters based on mass transfer phenomena. The axial dispersion coefficient (D L ) and group of dimensionless numbers; including Renold number (Re), Schmidt number (Sc), and Sherwood number (Sh) were all determined and correlated by Wilson-Geankoplis correlation that was used to estimate the external film diffusion coefficients (Kc) at 0.0015 < Re<55. Copyright © 2017 Elsevier Inc. All rights reserved.

Self-correcting random number generator

Science.gov (United States)

Humble, Travis S.; Pooser, Raphael C.

2016-09-06

A system and method for generating random numbers. The system may include a random number generator (RNG), such as a quantum random number generator (QRNG) configured to self-correct or adapt in order to substantially achieve randomness from the output of the RNG. By adapting, the RNG may generate a random number that may be considered random regardless of whether the random number itself is tested as such. As an example, the RNG may include components to monitor one or more characteristics of the RNG during operation, and may use the monitored characteristics as a basis for adapting, or self-correcting, to provide a random number according to one or more performance criteria.

2016 Gainesville Number Theory Conference

CERN Document Server

Garvan, Frank

2017-01-01

Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory.  Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find th...

Effect of junction configurations on microdroplet formation in a T-junction microchannel

Science.gov (United States)

Lih, F. L.; Miao, J. M.

2015-03-01

This study investigates the dynamic formation process of water microdroplets in a silicon oil flow in a T-junction microchannel. Segmented water microdroplets are formed at the junction when the water flow is perpendicularly injected into the silicon oil flow in a straight rectangular microchannel. This study further presents the effects of the water flow inlet geometry on hydrodynamic characteristics of water microdroplet formation. A numerical multiphase volume of fluid (VOF) scheme is coupled to solve the unsteady three-dimensional laminar Navier-Stokes equations to depict the droplet formation phenomena at the junction. Predicted results on the length and generated frequency of the microdroplets agree well with experimental results in a T-junction microchannel with straight and flat inlets (the base model) for both fluid flows. Empirical correlations are reported between the volumetric flow ratio and the dimensionless microdroplet length or dimensionless frequency of droplet generation at a fixed capillary number of 4.7 · 10-3. The results of this study indicate a reduction in the droplet length of approximately 21% if the straight inlet for the water flow is modified to a downstream sudden contraction inlet for the water flow.

Thermal stresses at nozzles of nuclear steel containments under LOCA-conditions

International Nuclear Information System (INIS)

Sanchez Sarmiento, G.; Bergmann, A.N.

1986-01-01

During a loss of coolant accident (LOCA) of a PWR-nuclear power plant, a considerable heating of the containment atmosphere is expected to occur. Transient thermal stresses will appear at the containment as a consequence of a non-uniform rise of its temperature. Applying computer codes based on the finite element method, dimensionless general thermal stresses at nozzles of spherical steel containment have been calculated, varying the principal geometrical parameters and the Biot number for the containment internal surface. Atmosphere temperature and Biot number are assumed constant after the accident. Several plots of the maximum principal stresses are provided, which constitute general results applicable to stress analysis of any particular containment of this kind. (orig.)

Experimental study on saturated boiling of two phase natural circulation under low pressure in narrow rectangular channels

Energy Technology Data Exchange (ETDEWEB)

Li, Zi-chao; Qi, Shi; Zhou, Tao; Li, Bing; Shahzad, Muhammad Ali [North China Electric Power Univ., Beijing (China). School of Nuclear Science and Engineering; Beijing Key Laboratory of Passive Safety Technology for Nuclear Energy, Beijing (China); Huang, Yan-ping [Nuclear Reactor Thermal Hydraulics Technology, Chengdu (China). CNNC Key Lab.

2017-12-15

Saturated boiling of two-phase natural circulation has been experimentally investigated based on a natural circulation device with narrow rectangular channels. When heating power reaches a certain range, it is possible to observe the phenomenon of saturated boiling and flow pattern transition in the system. The results show the heat transfer coefficient of saturated boiling decreases with the increasing of pressure, heating power and size of narrow rectangle channels. The buoyancy force causing mixed convection decreases the heat transfer coefficient. Finally, a dimensionless number is introduced, which reflects length to width ratio of rectangular narrow section and Rayleigh number, in order to revise the presented correlation. All errors fall within the range of ±15%.

An analytical model for non-conservative pollutants mixing in the surf zone.

Science.gov (United States)

Ki, Seo Jin; Hwang, Jin Hwan; Kang, Joo-Hyon; Kim, Joon Ha

2009-01-01

Accurate simulation of the surf zone is a prerequisite to improve beach management as well as to understand the fundamentals of fate and transport of contaminants. In the present study, a diagnostic model modified from a classic solute model is provided to illuminate non-conservative pollutants behavior in the surf zone. To readily understand controlling processes in the surf zone, a new dimensionless quantity is employed with index of kappa number (K, a ratio of inactivation rate to transport rate of microbial pollutant in the surf zone), which was then evaluated under different environmental frames during a week simulation period. The sensitivity analysis showed that hydrodynamics and concentration gradients in the surf zone mostly depend on n (number of rip currents), indicating that n should be carefully adjusted in the model. The simulation results reveal, furthermore, that large deviation typically occurs in the daytime, signifying inactivation of fecal indicator bacteria is the main process to control surf zone water quality during the day. Overall, the analytical model shows a good agreement between predicted and synthetic data (R(2) = 0.51 and 0.67 for FC and ENT, respectively) for the simulated period, amplifying its potential use in the surf zone modelling. It is recommended that when the dimensionless index is much larger than 0.5, the present modified model can predict better than the conventional model, but if index is smaller than 0.5, the conventional model is more efficient with respect to time and cost.

Random number generation and creativity.

Science.gov (United States)

Bains, William

2008-01-01

A previous paper suggested that humans can generate genuinely random numbers. I tested this hypothesis by repeating the experiment with a larger number of highly numerate subjects, asking them to call out a sequence of digits selected from 0 through 9. The resulting sequences were substantially non-random, with an excess of sequential pairs of numbers and a deficit of repeats of the same number, in line with previous literature. However, the previous literature suggests that humans generate random numbers with substantial conscious effort, and distractions which reduce that effort reduce the randomness of the numbers. I reduced my subjects' concentration by asking them to call out in another language, and with alcohol - neither affected the randomness of their responses. This suggests that the ability to generate random numbers is a 'basic' function of the human mind, even if those numbers are not mathematically 'random'. I hypothesise that there is a 'creativity' mechanism, while not truly random, provides novelty as part of the mind's defence against closed programming loops, and that testing for the effects seen here in people more or less familiar with numbers or with spontaneous creativity could identify more features of this process. It is possible that training to perform better at simple random generation tasks could help to increase creativity, through training people to reduce the conscious mind's suppression of the 'spontaneous', creative response to new questions.

Condensation heat transfer correlation for water-ethanol vapor mixture flowing through a plate heat exchanger

Science.gov (United States)

Zhou, Weiqing; Hu, Shenhua; Ma, Xiangrong; Zhou, Feng

2018-04-01

Condensation heat transfer coefficient (HTC) as a function of outlet vapor quality was investigated using water-ethanol vapor mixture of different ethanol vapor concentrations (0%, 1%, 2%, 5%, 10%, 20%) under three different system pressures (31 kPa, 47 kPa, 83 kPa). A heat transfer coefficient was developed by applying multiple linear regression method to experimental data, taking into account the dimensionless numbers which represents the Marangoni condensation effects, such as Re, Pr, Ja, Ma and Sh. The developed correlation can predict the condensation performance within a deviation range from -22% to 32%. Taking PHE's characteristic into consideration and bringing in Ma number and Sh number, a new correlation was developed, which showed a much more accurate prediction, within a deviation from -3.2% to 7.9%.

Constructal design of finned tubes used in air-cooled heat exchangers

Energy Technology Data Exchange (ETDEWEB)

Shokouhmand, Hossein; Mahjoub, Shoeib [University of Tehran, Tehran (Iran, Islamic Republic of); Salimpour, Mohammad Reza [Isfahan University of Technology, Isfahan (Iran, Islamic Republic of)

2014-06-15

The present study documents the constructal design and optimization of finned tubes used in air-cooled heat exchangers. The considered tubes are equipped with annular fins. The aim is to minimize the overall thermal resistance by morphing the geometry. The geometrical and thermo-physical parameters considered are the number of fins, ratio of fin height to tube diameter, Stanton number, ratio of fin conductivity to air conductivity, ratio of in-tube fluid conductivity to air conductivity and dimensionless pressure drop. Two constraints are applied in the optimization process: fixed overall volume of heat exchanger and fixed volume fraction of fin material. It is found that there exist optimal values for the number and the height of fins. Moreover, the optimal heat transfer has an extremum in a special volume fraction of fin material.

Constructal design of finned tubes used in air-cooled heat exchangers

International Nuclear Information System (INIS)

Shokouhmand, Hossein; Mahjoub, Shoeib; Salimpour, Mohammad Reza

2014-01-01

The present study documents the constructal design and optimization of finned tubes used in air-cooled heat exchangers. The considered tubes are equipped with annular fins. The aim is to minimize the overall thermal resistance by morphing the geometry. The geometrical and thermo-physical parameters considered are the number of fins, ratio of fin height to tube diameter, Stanton number, ratio of fin conductivity to air conductivity, ratio of in-tube fluid conductivity to air conductivity and dimensionless pressure drop. Two constraints are applied in the optimization process: fixed overall volume of heat exchanger and fixed volume fraction of fin material. It is found that there exist optimal values for the number and the height of fins. Moreover, the optimal heat transfer has an extremum in a special volume fraction of fin material.

Exergoeconomic performance optimization of an endoreversible intercooled regenerative Brayton combined heat and power plant coupled to variable-temperature heat reservoirs

Energy Technology Data Exchange (ETDEWEB)

Yang, Bo; Chen, Lingen; Sun, Fengrui [College of Naval Architecture and Power, Naval University of Engineering, Wuhan 430033 (China)

2012-07-01

An endoreversible intercooled regenerative Brayton combined heat and power (CHP) plant model coupled to variable-temperature heat reservoirs is established. The exergoeconomic performance of the CHP plant is investigated using finite time thermodynamics. The analytical formulae about dimensionless profit rate and exergy efficiency of the CHP plant with the heat resistance losses in the hot-, cold- and consumer-side heat exchangers, the intercooler and the regenerator are deduced. By taking the maximum profit rate as the objective, the heat conductance allocation among the five heat exchangers and the choice of intercooling pressure ratio are optimized by numerical examples, the characteristic of the optimal dimensionless profit rate versus corresponding exergy efficiency is investigated. When the optimization is performed further with respect to the total pressure ratio, a double-maximum profit rate is obtained. The effects of the design parameters on the double-maximum dimensionless profit rate and corresponding exergy efficiency, optimal total pressure ratio and optimal intercooling pressure ratio are analyzed in detail, and it is found that there exist an optimal consumer-side temperature and an optimal thermal capacitance rate matching between the working fluid and the heat reservoir, respectively, corresponding to a thrice-maximum dimensionless profit rate.

Coexistence properties of the Redlich-Kwong model for a fluid

International Nuclear Information System (INIS)

Pina, Eduardo; Selva, Sara MarIa Teresa de la

2006-01-01

It is shown in this paper that for pure substances obeying the van der Waals (VdW) equation of state (EOS) or Redlich-Kwong (RK) type equations of state below the critical temperature, it is possible to obtain with the help of the Maxwell equal areas rule the vapour pressure curve, the difference between the molar volume of the vapour and of the liquid, and the difference between the molar entropies of vapour and liquid; each property is obtained in the first step as a dimensionless expression, function of a dimensionless temperature. Any particular property of a particular fluid obeying VdW EOS or one type of RK EOS can be obtained from the corresponding dimensionless expression by multiplying it with a dimension unit which is a function of the particular temperature-dependent parameter a(T) of the EOS considered for the fluid. In the cases of VdW and the original RK (EOS), the dimensionless functions are unique for all the pure fluids that obey the EOS under consideration. A comparison of VdW, RK and RK-Soave (SRK) predictions with experimental vapour pressure data is exemplified for carbon dioxide

Performance assessment and optimization of an irreversible nano-scale Stirling engine cycle operating with Maxwell-Boltzmann gas

Science.gov (United States)

Ahmadi, Mohammad H.; Ahmadi, Mohammad-Ali; Pourfayaz, Fathollah

2015-09-01

Developing new technologies like nano-technology improves the performance of the energy industries. Consequently, emerging new groups of thermal cycles in nano-scale can revolutionize the energy systems' future. This paper presents a thermo-dynamical study of a nano-scale irreversible Stirling engine cycle with the aim of optimizing the performance of the Stirling engine cycle. In the Stirling engine cycle the working fluid is an Ideal Maxwell-Boltzmann gas. Moreover, two different strategies are proposed for a multi-objective optimization issue, and the outcomes of each strategy are evaluated separately. The first strategy is proposed to maximize the ecological coefficient of performance (ECOP), the dimensionless ecological function (ecf) and the dimensionless thermo-economic objective function ( F . Furthermore, the second strategy is suggested to maximize the thermal efficiency ( η), the dimensionless ecological function (ecf) and the dimensionless thermo-economic objective function ( F). All the strategies in the present work are executed via a multi-objective evolutionary algorithms based on NSGA∥ method. Finally, to achieve the final answer in each strategy, three well-known decision makers are executed. Lastly, deviations of the outcomes gained in each strategy and each decision maker are evaluated separately.

A new method for pressure test analysis of a vertically fractured well producing commingled zones in bounded square reservoirs

Energy Technology Data Exchange (ETDEWEB)

Osman, Mohammed E.; Abou-Kassem, J.H. [Chemical and Petroleum Engineering Department, UAE University, Al-Ain (United Arab Emirates)

1997-07-15

Although hydraulically or naturally fractured wells located in stratified bounded reservoirs are common, reliable techniques available to analyze the pressure test data for such reservoirs are lacking. This paper presents a mathematical model that describes the pressure behavior of a vertically fractured well located in a stratified, bounded, square reservoir. The fracture can be either a uniform flux or an infinite conductivity fracture. It was found that the dimensionless pressure function and its derivative and the fractional production rate from the different layers are mainly controlled by the fracture penetration into the formation, and that transmissibility and storativity affect the fractional production rate and the pressure derivative but have little effect on the dimensionless pressure function. Type curves of dimensionless pressure and dimensionless pressure derivative can be used to evaluate the reservoir characteristics. The selection of the appropriate type curve is guided by the behavior of the layer fractional production rate obtained from flow rate survey carried out during well testing. Type curves for uniform flux and infinite conductivity fractures exhibit similar features. Two examples are presented to demonstrate the application of the new method of analysis presented in this paper

Nominal power density analysis of thermoelectric pins with non-constant cross sections

International Nuclear Information System (INIS)

Shi, Yaoguang; Mei, Deqing; Yao, Zhehe; Wang, Yancheng; Liu, Haiyan; Chen, Zichen

2015-01-01

Highlights: • Nominal power density of TEGs with non-constant cross sections pins is analyzed. • An analytical model of nominal power density (NPD) is developed. • Influences of shape parameter on NPD for different geometric pins are investigated. • Effects of dimensionless efficiency and the temperature ratio on NPD are examined. - Abstract: The investigation of the geometric structure of TEG (thermoelectric generator) pins is essential, as their geometry determines the performance of devices. In this study, nominal power density (NPD) is used to find a better geometric structure of thermoelectric pins of TEGs, since a comparison of maximum dimensionless efficiencies for different geometric pins cannot be used to identify the optimum geometry. The influence of shape parameter on NPD for TEG pins in linear, quadratic and exponential cross-sectional functions is studied. The NPD decreases when the shape parameter increases for different geometric pins, while the maximum values of NPD are the same. Then, the effects of dimensionless efficiency and the temperature ratio on the NPD are analyzed. The NPD decreases with the increase in dimensionless efficiency and temperature ratio. Pins with linear variation in cross section have the highest NPD among the three geometries of pins evaluated

Development of two phase turbulent mixing model for subchannel analysis relevant to BWR

International Nuclear Information System (INIS)

Sharma, M.P.; Nayak, A.K.; Kannan, Umasankari

2014-01-01

A two phase flow model is presented, which predicts both liquid and gas phase turbulent mixing rate between adjacent subchannels of reactor rod bundles. The model presented here is for slug churn flow regime, which is dominant as compared to the other regimes like bubbly flow and annular flow regimes, since turbulent mixing rate is the highest in slug churn flow regime. In this paper, we have defined new dimensionless parameters i.e. liquid mixing number and gas mixing number for two phase turbulent mixing. The liquid mixing number is a function of mixture Reynolds number whereas the gas phase mixing number is a function of both mixture Reynolds number and volumetric fraction of gas. The effect of pressure, geometrical influence of subchannel is also included in this model. The present model has been tested against low pressure and temperature air-water and high pressure and temperature steam-water experimental data found that it shows good agreement with available experimental data. (author)

Positive approach: Implications for the relation between number theory and geometry, including connection to Santilli mathematics, from Fibonacci reconstitution of natural numbers and of prime numbers

International Nuclear Information System (INIS)

Johansen, Stein E.

2014-01-01

The paper recapitulates some key elements in previously published results concerning exact and complete reconstitution of the field of natural numbers, both as ordinal and as cardinal numbers, from systematic unfoldment of the Fibonacci algorithm. By this natural numbers emerge as Fibonacci 'atoms' and 'molecules' consistent with the notion of Zeckendorf sums. Here, the sub-set of prime numbers appears not as the primary numbers, but as an epistructure from a deeper Fibonacci constitution, and is thus targeted from a 'positive approach'. In the Fibonacci reconstitution of number theory natural numbers show a double geometrical aspect: partly as extension in space and partly as position in a successive structuring of space. More specifically, the natural numbers are shown to be distributed by a concise 5:3 code structured from the Fibonacci algorithm via Pascal's triangle. The paper discusses possible implications for the more general relation between number theory and geometry, as well as more specifically in relation to hadronic mathematics, initiated by R.M. Santilli, and also briefly to some other recent science linking number theory more directly to geometry and natural systems

Positive approach: Implications for the relation between number theory and geometry, including connection to Santilli mathematics, from Fibonacci reconstitution of natural numbers and of prime numbers

Energy Technology Data Exchange (ETDEWEB)

Johansen, Stein E., E-mail: stein.johansen@svt.ntnu.no [Institute for Basic Research, Division of Physics, Palm Harbor, Florida, USA and Norwegian University of Science and Technology, Department of Social Anthropology, Trondheim (Norway)

2014-12-10

The paper recapitulates some key elements in previously published results concerning exact and complete reconstitution of the field of natural numbers, both as ordinal and as cardinal numbers, from systematic unfoldment of the Fibonacci algorithm. By this natural numbers emerge as Fibonacci 'atoms' and 'molecules' consistent with the notion of Zeckendorf sums. Here, the sub-set of prime numbers appears not as the primary numbers, but as an epistructure from a deeper Fibonacci constitution, and is thus targeted from a 'positive approach'. In the Fibonacci reconstitution of number theory natural numbers show a double geometrical aspect: partly as extension in space and partly as position in a successive structuring of space. More specifically, the natural numbers are shown to be distributed by a concise 5:3 code structured from the Fibonacci algorithm via Pascal's triangle. The paper discusses possible implications for the more general relation between number theory and geometry, as well as more specifically in relation to hadronic mathematics, initiated by R.M. Santilli, and also briefly to some other recent science linking number theory more directly to geometry and natural systems.

Neutrino number of the universe

International Nuclear Information System (INIS)

Kolb, E.W.

1981-01-01

The influence of grand unified theories on the lepton number of the universe is reviewed. A scenario is presented for the generation of a large (>> 1) lepton number and a small (<< 1) baryon number. 15 references

Distribution theory of algebraic numbers

CERN Document Server

Yang, Chung-Chun

2008-01-01

The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions Algebraic numbers Algebraic geometry Height functions The abc-conjecture Roth''s theorem Subspace theorems Vojta''s conjectures L-functions.

Quantum random number generator

Science.gov (United States)

Pooser, Raphael C.

2016-05-10

A quantum random number generator (QRNG) and a photon generator for a QRNG are provided. The photon generator may be operated in a spontaneous mode below a lasing threshold to emit photons. Photons emitted from the photon generator may have at least one random characteristic, which may be monitored by the QRNG to generate a random number. In one embodiment, the photon generator may include a photon emitter and an amplifier coupled to the photon emitter. The amplifier may enable the photon generator to be used in the QRNG without introducing significant bias in the random number and may enable multiplexing of multiple random numbers. The amplifier may also desensitize the photon generator to fluctuations in power supplied thereto while operating in the spontaneous mode. In one embodiment, the photon emitter and amplifier may be a tapered diode amplifier.

Professor Stewart's incredible numbers

CERN Document Server

Stewart, Ian

2015-01-01

Ian Stewart explores the astonishing properties of numbers from 1 to10 to zero and infinity, including one figure that, if you wrote it out, would span the universe. He looks at every kind of number you can think of - real, imaginary, rational, irrational, positive and negative - along with several you might have thought you couldn't think of. He explains the insights of the ancient mathematicians, shows how numbers have evolved through the ages, and reveals the way numerical theory enables everyday life. Under Professor Stewart's guidance you will discover the mathematics of codes,

Elementary theory of numbers

CERN Document Server

Sierpinski, Waclaw

1988-01-01

Since the publication of the first edition of this work, considerable progress has been made in many of the questions examined. This edition has been updated and enlarged, and the bibliography has been revised.The variety of topics covered here includes divisibility, diophantine equations, prime numbers (especially Mersenne and Fermat primes), the basic arithmetic functions, congruences, the quadratic reciprocity law, expansion of real numbers into decimal fractions, decomposition of integers into sums of powers, some other problems of the additive theory of numbers and the theory of Gaussian

Fundamentals of number theory

CERN Document Server

LeVeque, William J

1996-01-01

This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given - making the book self-contained in this respect.The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diopha

Generalized r-Lah numbers

Indian Academy of Sciences (India)

016-0309-0. Generalized r-Lah numbers. MARK SHATTUCK. Department of ...... of Dowling lattices, Discrete Math. 312. (2012) 2337–2348. [7] Hsu L C and Shiue P J-S, A unified approach to generalized Stirling numbers, Adv. Appl. Math.

The theory of algebraic numbers

CERN Document Server

Pollard, Harry

1998-01-01

An excellent introduction to the basics of algebraic number theory, this concise, well-written volume examines Gaussian primes; polynomials over a field; algebraic number fields; and algebraic integers and integral bases. After establishing a firm introductory foundation, the text explores the uses of arithmetic in algebraic number fields; the fundamental theorem of ideal theory and its consequences; ideal classes and class numbers; and the Fermat conjecture. 1975 edition. References. List of Symbols. Index.

Effects of chemical reaction on moving isothermal vertical plate with variable mass diffusion

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2003-01-01

Full Text Available An exact solution to the problem of flow past an impulsively started infinite vertical isothermal plate with variable mass diffusion is presented here, taking into account of the homogeneous chemical reaction of first-order. The dimensionless governing equations are solved by using the Laplace - transform technique. The velocity and skin-friction are studied for different parameters like chemical reaction parameter, Schmidt number and buoyancy ratio parameter. It is observed that the veloc­ity increases with decreasing chemical reaction parameter and increases with increasing buoyancy ratio parameter.

Thermal hydraulic phenomena in corium pools: the BALI experiment

International Nuclear Information System (INIS)

Bonnet, J.M.

1999-01-01

In the framework of severe accident studies, the BALI experiment has been designed to create a data base about heat transfer distribution at corium pool boundaries for in-vessel or ex-vessel configurations. The mechanism investigated is natural convection at high internal Rayleigh number (10 15 to 10 17 ) in cavities with volumetric heating. After a description of the facility and a synthesis of results obtained for in-vessel configurations, the purpose of this paper is to present or extend local or average heat transfer correlations in the prototypic range of dimensionless parameters. (author)

Permeation of hydrogen through metal membranes

International Nuclear Information System (INIS)

Wienhold, P.; Rota, E.; Waelbroeck, F.; Winter, J.; Banno, Tatsuya.

1986-08-01

Experiments show that the permeant flux of hydrogen through a metal membrane at low driving pressures ( r is introduced into the model as a new material constant and the rate equations are given. After the description of the wall pump effect, a variety of different limiting cases are discussed for a symmetrical permeation membrane. This is modified to the asymmetric case and to the influence of particle implantation. The permeation number W turns out to be a dimensionless quantity which characterizes the permeation range and predicts the permeant flux in steady state. (orig.)

A model of the fluid temperature field in a turbulent flow parallel to heated tube bundle

International Nuclear Information System (INIS)

Carvalho Tofani, P. de.

1986-01-01

Basic understanding of thermal-hydraulic phenomena is essential to achieving reactor fuel assembly performance analysis. In this paper, a dimensionless parameter - a normalized fluid temperature - is defined and applied to fluid temperature measurements at particular positions at the exit plane of a bank of nine heated tubes, under different transverse heat flux shapes. This parameter presents an asymptotic trend to equilibrium values, which depend upon considered positions and flux shapes; when increasing the bulk Reynolds Number. Proposed correlations underlie the present approach to predict the fluid temperature field within the tube bundle. (Author) [pt

Henry constants in polymer solutions with the van der Waals equation of state

DEFF Research Database (Denmark)

Bithas, Sotiris; Kalospiros, Nikolaos; Kontogeorgis, Georgios

1996-01-01

parameter is satisfactory, with typical errors within the experimental uncertainty and comparable to those with the more complex Perturbed Hard Chain Theory-based equations of state with the same number of adjustable parameters. A predictive scheme for calculating Henry constants is also presented, which...... is a corresponding-states correlation for a dimensionless Henry constant defined based on the van der Waals equation of state. Satisfactory results-often close to the ones from the one-parameter correlation-are obtained for all systems investigated in this work. Compared with literature models that have been applied...

On soft stability loss in rotating turbulent MHD flows

International Nuclear Information System (INIS)

Kapusta, Arkady; Mikhailovich, Boris

2014-01-01

The problem of the stability of turbulent flows of liquid metal in a cylindrical cavity against small velocity disturbances under the action of a rotating magnetic field (RMF) has been studied. The flow is considered in the induction-free approximation using the ‘external’ friction model. A system of dimensionless equations is examined in cylindrical coordinates. The results of computations performed on the basis of this mathematical model using the exchange of stabilities principle have shown a good consistency between the critical values of computed and experimental Reynolds numbers. (paper)

Theoretical research on laminar friction resistance in tubes in rolling motion

International Nuclear Information System (INIS)

Yan Binghuo; Yu Lei; Yang Yanhua

2010-01-01

The model of laminar flow in tubes in rolling motion is established. The dimensionless correlation of velocity is derived, and the correlation of frictional resistance coefficient is also obtained. Of all the additional forces, only the tangential force effects on the flow. The effect of centrifugal and Coriolis forces on the flow is counteracted. The correlation of average frictional resistance coefficient is the same with that of no rolling motion. The effect of rolling motion on frictional resistance coefficient of laminar flow diminishes with the increase of Reynolds number. (authors)

Current sheets in the Earth’s magnetosphere and in laboratory experiments: The magnetic field structure and the Hall effect

International Nuclear Information System (INIS)

Frank, A. G.; Artemyev, A. V.; Zelenyi, L. M.

2016-01-01

The main characteristics of current sheets (CSs) formed in laboratory experiments are compared with the results of satellite observations of CSs in the Earth’s magnetotail. We show that many significant features of the magnetic field structure and the distributions of plasma parameters in laboratory and magnetospheric CSs exhibit a qualitative similarity, despite the enormous differences of scales, absolute values of plasma parameters, magnetic fields, and currents. In addition to a qualitative comparison, we give a number of dimensionless parameters that demonstrate the possibility of laboratory modeling of the processes occurring in the magnetosphere.

Assessment of capabilities of lidar systems in day-and night-time under different atmospheric and internal-noise conditions

Science.gov (United States)

Agishev, Ravil; Comerón, Adolfo

2018-04-01

As an application of the dimensionless parameterization concept proposed earlier for the characterization of lidar systems, the universal assessment of lidar capabilities in day and night conditions is considered. The dimensionless parameters encapsulate the atmospheric conditions, the lidar optical and optoelectronic characteristics, including the photodetector internal noise, and the sky background radiation. Approaches to ensure immunity of the lidar system to external background radiation are discussed.

Innate or Acquired? – Disentangling Number Sense and Early Number Competencies

Directory of Open Access Journals (Sweden)

Julia Siemann

2018-04-01

Full Text Available The clinical profile termed developmental dyscalculia (DD is a fundamental disability affecting children already prior to arithmetic schooling, but the formal diagnosis is often only made during school years. The manifold associated deficits depend on age, education, developmental stage, and task requirements. Despite a large body of studies, the underlying mechanisms remain dubious. Conflicting findings have stimulated opposing theories, each presenting enough empirical support to remain a possible alternative. A so far unresolved question concerns the debate whether a putative innate number sense is required for successful arithmetic achievement as opposed to a pure reliance on domain-general cognitive factors. Here, we outline that the controversy arises due to ambiguous conceptualizations of the number sense. It is common practice to use early number competence as a proxy for innate magnitude processing, even though it requires knowledge of the number system. Therefore, such findings reflect the degree to which quantity is successfully transferred into symbols rather than informing about quantity representation per se. To solve this issue, we propose a three-factor account and incorporate it into the partly overlapping suggestions in the literature regarding the etiology of different DD profiles. The proposed view on DD is especially beneficial because it is applicable to more complex theories identifying a conglomerate of deficits as underlying cause of DD.

Innate or Acquired? – Disentangling Number Sense and Early Number Competencies

Science.gov (United States)

Siemann, Julia; Petermann, Franz

2018-01-01

The clinical profile termed developmental dyscalculia (DD) is a fundamental disability affecting children already prior to arithmetic schooling, but the formal diagnosis is often only made during school years. The manifold associated deficits depend on age, education, developmental stage, and task requirements. Despite a large body of studies, the underlying mechanisms remain dubious. Conflicting findings have stimulated opposing theories, each presenting enough empirical support to remain a possible alternative. A so far unresolved question concerns the debate whether a putative innate number sense is required for successful arithmetic achievement as opposed to a pure reliance on domain-general cognitive factors. Here, we outline that the controversy arises due to ambiguous conceptualizations of the number sense. It is common practice to use early number competence as a proxy for innate magnitude processing, even though it requires knowledge of the number system. Therefore, such findings reflect the degree to which quantity is successfully transferred into symbols rather than informing about quantity representation per se. To solve this issue, we propose a three-factor account and incorporate it into the partly overlapping suggestions in the literature regarding the etiology of different DD profiles. The proposed view on DD is especially beneficial because it is applicable to more complex theories identifying a conglomerate of deficits as underlying cause of DD. PMID:29725316

Dynamic Virtual Credit Card Numbers

Science.gov (United States)

Molloy, Ian; Li, Jiangtao; Li, Ninghui

Theft of stored credit card information is an increasing threat to e-commerce. We propose a dynamic virtual credit card number scheme that reduces the damage caused by stolen credit card numbers. A user can use an existing credit card account to generate multiple virtual credit card numbers that are either usable for a single transaction or are tied with a particular merchant. We call the scheme dynamic because the virtual credit card numbers can be generated without online contact with the credit card issuers. These numbers can be processed without changing any of the infrastructure currently in place; the only changes will be at the end points, namely, the card users and the card issuers. We analyze the security requirements for dynamic virtual credit card numbers, discuss the design space, propose a scheme using HMAC, and prove its security under the assumption the underlying function is a PRF.

From natural numbers to quaternions

CERN Document Server

Kramer, Jürg

2017-01-01

This textbook offers an invitation to modern algebra through number systems of increasing complexity, beginning with the natural numbers and culminating with Hamilton's quaternions. Along the way, the authors carefully develop the necessary concepts and methods from abstract algebra: monoids, groups, rings, fields, and skew fields. Each chapter ends with an appendix discussing related topics from algebra and number theory, including recent developments reflecting the relevance of the material to current research. The present volume is intended for undergraduate courses in abstract algebra or elementary number theory. The inclusion of exercises with solutions also makes it suitable for self-study and accessible to anyone with an interest in modern algebra and number theory.

Elementary number theory with programming

CERN Document Server

Lewinter, Marty

2015-01-01

A successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and con

Parameter estimation for an expanding universe

Directory of Open Access Journals (Sweden)

Jieci Wang

2015-03-01

Full Text Available We study the parameter estimation for excitations of Dirac fields in the expanding Robertson–Walker universe. We employ quantum metrology techniques to demonstrate the possibility for high precision estimation for the volume rate of the expanding universe. We show that the optimal precision of the estimation depends sensitively on the dimensionless mass m˜ and dimensionless momentum k˜ of the Dirac particles. The optimal precision for the ratio estimation peaks at some finite dimensionless mass m˜ and momentum k˜. We find that the precision of the estimation can be improved by choosing the probe state as an eigenvector of the hamiltonian. This occurs because the largest quantum Fisher information is obtained by performing projective measurements implemented by the projectors onto the eigenvectors of specific probe states.

Personal number Management : personal numbers and identity fraud – number strategies for security and privacy in an information society - part 1

NARCIS (Netherlands)

Grijpink, J.H.A.M.

2002-01-01

For the sake of clarity and manageability, this article is in the form of a checklist. It will be published in two parts. The first part in this issue presents some practical and juridical characteristics of personal number systems. But at the end of the day, it is the number strategy that

How to be Brilliant at Numbers

CERN Document Server

Webber, Beryl

2010-01-01

How to be Brilliant at Numbers will help students to develop an understanding of numbers, place value, fractions and decimals. They will develop the language of number, and of the relationships between numbers. They will also use mathematics to solve problems and will develop mathematical reasoning. Using the worksheets in this book, pupils will learn about: ancient Greek numbers; coins; digits; consecutive numbers; magic ladders; fractions; matching pairs; multiples of 10; rounding; decimal un

Unsolved problems in number theory

CERN Document Server

Guy, Richard K

1994-01-01

Unsolved Problems in Number Theory contains discussions of hundreds of open questions, organized into 185 different topics. They represent numerous aspects of number theory and are organized into six categories: prime numbers, divisibility, additive number theory, Diophantine equations, sequences of integers, and miscellaneous. To prevent repetition of earlier efforts or duplication of previously known results, an extensive and up-to-date collection of references follows each problem. In the second edition, not only extensive new material has been added, but corrections and additions have been included throughout the book.

Prandtl number of toroidal plasmas

International Nuclear Information System (INIS)

Itoh, K.; Itoh, S.; Fukuyama, A.; Yagi, M.; Azumi, M.

1993-06-01

Theory of the L-mode confinement in toroidal plasmas is developed. The Prandtl number, the ratio between the ion viscosity and the thermal conductivity is obtained for the anomalous transport process which is caused by the self-sustained turbulence in the toroidal plasma. It is found that the Prandtl number is of order unity both for the ballooning mode turbulence in tokamaks and for the interchange mode turbulence in helical system. The influence on the anomalous transport and fluctuation level is evaluated. Hartmann number and magnetic Prandtl number are also discussed. (author)

Quantum random number generator

Science.gov (United States)

Soubusta, Jan; Haderka, Ondrej; Hendrych, Martin

2001-03-01

Since reflection or transmission of a quantum particle on a beamsplitter is inherently random quantum process, a device built on this principle does not suffer from drawbacks of neither pseudo-random computer generators or classical noise sources. Nevertheless, a number of physical conditions necessary for high quality random numbers generation must be satisfied. Luckily, in quantum optics realization they can be well controlled. We present an easy random number generator based on the division of weak light pulses on a beamsplitter. The randomness of the generated bit stream is supported by passing the data through series of 15 statistical test. The device generates at a rate of 109.7 kbit/s.

The emergence of number

CERN Document Server

Crossley, John N

1987-01-01

This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of Gödel's theorem. The second part is concerned with the deve

Brief history of numbers

CERN Document Server

Corry, Leo

2015-01-01

The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the

Earthquake number forecasts testing

Science.gov (United States)

Kagan, Yan Y.

2017-10-01

We study the distributions of earthquake numbers in two global earthquake catalogues: Global Centroid-Moment Tensor and Preliminary Determinations of Epicenters. The properties of these distributions are especially required to develop the number test for our forecasts of future seismic activity rate, tested by the Collaboratory for Study of Earthquake Predictability (CSEP). A common assumption, as used in the CSEP tests, is that the numbers are described by the Poisson distribution. It is clear, however, that the Poisson assumption for the earthquake number distribution is incorrect, especially for the catalogues with a lower magnitude threshold. In contrast to the one-parameter Poisson distribution so widely used to describe earthquake occurrences, the negative-binomial distribution (NBD) has two parameters. The second parameter can be used to characterize the clustering or overdispersion of a process. We also introduce and study a more complex three-parameter beta negative-binomial distribution. We investigate the dependence of parameters for both Poisson and NBD distributions on the catalogue magnitude threshold and on temporal subdivision of catalogue duration. First, we study whether the Poisson law can be statistically rejected for various catalogue subdivisions. We find that for most cases of interest, the Poisson distribution can be shown to be rejected statistically at a high significance level in favour of the NBD. Thereafter, we investigate whether these distributions fit the observed distributions of seismicity. For this purpose, we study upper statistical moments of earthquake numbers (skewness and kurtosis) and compare them to the theoretical values for both distributions. Empirical values for the skewness and the kurtosis increase for the smaller magnitude threshold and increase with even greater intensity for small temporal subdivision of catalogues. The Poisson distribution for large rate values approaches the Gaussian law, therefore its skewness

Improved lumped models for transient combined convective and radiative cooling of a two-layer spherical fuel element

International Nuclear Information System (INIS)

Silva, Alice Cunha da; Su, Jian

2013-01-01

The High Temperature Gas cooled Reactor (HTGR) is a fourth generation thermal nuclear reactor, graphite-moderated and helium cooled. The HTGRs have important characteristics making essential the study of these reactors, as well as its fuel element. Examples of these are: high thermal efficiency,low operating costs and construction, passive safety attributes that allow implication of the respective plants. The Pebble Bed Modular Reactor (PBMR) is a HTGR with spherical fuel elements that named the reactor. This fuel element is composed by a particulate region with spherical inclusions, the fuel UO2 particles, dispersed in a graphite matrix and a convective heat transfer by Helium happens on the outer surface of the fuel element. In this work, the transient heat conduction in a spherical fuel element of a pebble-bed high temperature reactor was studied in a transient situation of combined convective and radiative cooling. Improved lumped parameter model was developed for the transient heat conduction in the two-layer composite sphere subjected to combined convective and radiative cooling. The improved lumped model was obtained through two-point Hermite approximations for integrals. Transient combined convective and radiative cooling of the two-layer spherical fuel element was analyzed to illustrate the applicability of the proposed lumped model, with respect to die rent values of the Biot number, the radiation-conduction parameter, the dimensionless thermal contact resistance, the dimensionless inner diameter and coating thickness, and the dimensionless thermal conductivity. It was shown by comparison with numerical solution of the original distributed parameter model that the improved lumped model, with H2,1/H1,1/H0,0 approximation yielded significant improvement of average temperature prediction over the classical lumped model. (author)

Reduced-order model for inertial locomotion of a slender swimmer

Science.gov (United States)

Mahalinkam, Raksha; Gong, Felicity; Khair, Aditya S.

2018-04-01

The inertial locomotion of an elongated model swimmer in a Newtonian fluid is quantified, wherein self-propulsion is achieved via steady tangential surface treadmilling. The swimmer has a length 2 l and a circular cross section of longitudinal profile a R (z ) , where a is the characteristic width of the cross section, R (z ) is a dimensionless shape function, and z is a dimensionless coordinate, normalized by l , along the centerline of the body. It is assumed that the swimmer is slender, ɛ =a /l ≪1 . Hence, we utilize slender-body theory to analyze the Navier-Stokes equations that describe the flow around the swimmer. Therefrom, we compute an asymptotic approximation to the swimming speed, U , as U /us=1 -β [V (Re ) -1/2 ∫-11z lnR (z ) d z ] /ln(1 /ɛ ) +O [1 /ln2(1 /ɛ ) ], where us is the characteristic speed of the surface treadmilling, Re is the Reynolds number based on the body length, and β is a dimensionless parameter that differentiates between "pusher" (propelled from the rear, β 0 ) -type swimmers. The function V (Re ) increases monotonically with increasing Re ; hence, fluid inertia causes an increase (decrease) in the swimming speed of a pusher (puller). Next, we demonstrate that the power expenditure of the swimmer increases monotonically with increasing Re . Further, the power expenditures of a puller and pusher with the same value of |β | are equal. Therefore, pushers are superior in inertial locomotion as compared to pullers, in that they achieve a faster swimming speed for the same power expended. Finally, it is demonstrated that the flow structure predicted from our reduced-order model is consistent with that from direct numerical simulation of swimmers at intermediate Re .

Single-Fiber Reflectance Spectroscopy of Isotropic-Scattering Medium: An Analytic Perspective to the Ratio-of-Remission in Steady-State Measurements

Directory of Open Access Journals (Sweden)

Daqing Piao

2014-12-01

Full Text Available Recent focused Monte Carlo and experimental studies on steady-state single-fiber reflectance spectroscopy (SfRS from a biologically relevant scattering medium have revealed that, as the dimensionless reduced scattering of the medium increases, the SfRS intensity increases monotonically until reaching a plateau. The SfRS signal is semi-empirically decomposed to the product of three contributing factors, including a ratio-of-remission (RoR term that refers to the ratio of photons remitting from the medium and crossing the fiber-medium interface over the total number of photons launched into the medium. The RoR is expressed with respect to the dimensionless reduced scattering parameter , where  is the reduced scattering coefficient of the medium and  is the diameter of the probing fiber. We develop in this work, under the assumption of an isotropic-scattering medium, a method of analytical treatment that will indicate the pattern of RoR as a function of the dimensionless reduced scattering of the medium. The RoR is derived in four cases, corresponding to in-medium (applied to interstitial probing of biological tissue or surface-based (applied to contact-probing of biological tissue SfRS measurements using straight-polished or angle-polished fiber. The analytically arrived surface-probing RoR corresponding to single-fiber probing using a 15° angle-polished fiber over the range of  agrees with previously reported similarly configured experimental measurement from a scattering medium that has a Henyey–Greenstein scattering phase function with an anisotropy factor of 0.8. In cases of a medium scattering light anisotropically, we propose how the treatment may be furthered to account for the scattering anisotropy using the result of a study of light scattering close to the point-of-entry by Vitkin et al. (Nat. Commun. 2011, doi:10.1038/ncomms1599.

Optimal energy-utilization ratio for long-distance cruising of a model fish

Science.gov (United States)

Liu, Geng; Yu, Yong-Liang; Tong, Bing-Gang

2012-07-01

The efficiency of total energy utilization and its optimization for long-distance migration of fish have attracted much attention in the past. This paper presents theoretical and computational research, clarifying the above well-known classic questions. Here, we specify the energy-utilization ratio (fη) as a scale of cruising efficiency, which consists of the swimming speed over the sum of the standard metabolic rate and the energy consumption rate of muscle activities per unit mass. Theoretical formulation of the function fη is made and it is shown that based on a basic dimensional analysis, the main dimensionless parameters for our simplified model are the Reynolds number (Re) and the dimensionless quantity of the standard metabolic rate per unit mass (Rpm). The swimming speed and the hydrodynamic power output in various conditions can be computed by solving the coupled Navier-Stokes equations and the fish locomotion dynamic equations. Again, the energy consumption rate of muscle activities can be estimated by the quotient of dividing the hydrodynamic power by the muscle efficiency studied by previous researchers. The present results show the following: (1) When the value of fη attains a maximum, the dimensionless parameter Rpm keeps almost constant for the same fish species in different sizes. (2) In the above cases, the tail beat period is an exponential function of the fish body length when cruising is optimal, e.g., the optimal tail beat period of Sockeye salmon is approximately proportional to the body length to the power of 0.78. Again, the larger fish's ability of long-distance cruising is more excellent than that of smaller fish. (3) The optimal swimming speed we obtained is consistent with previous researchers’ estimations.

Are calanco landforms similar to river basins?

Science.gov (United States)

Caraballo-Arias, N A; Ferro, V

2017-12-15

In the past badlands have been often considered as ideal field laboratories for studying landscape evolution because of their geometrical similarity to larger fluvial systems. For a given hydrological process, no scientific proof exists that badlands can be considered a model of river basin prototypes. In this paper the measurements carried out on 45 Sicilian calanchi, a type of badlands that appears as a small-scale hydrographic unit, are used to establish their morphological similarity with river systems whose data are available in the literature. At first the geomorphological similarity is studied by identifying the dimensionless groups, which can assume the same value or a scaled one in a fixed ratio, representing drainage basin shape, stream network and relief properties. Then, for each property, the dimensionless groups are calculated for the investigated calanchi and the river basins and their corresponding scale ratio is evaluated. The applicability of Hack's, Horton's and Melton's laws for establishing similarity criteria is also tested. The developed analysis allows to conclude that a quantitative morphological similarity between calanco landforms and river basins can be established using commonly applied dimensionless groups. In particular, the analysis showed that i) calanchi and river basins have a geometrically similar shape respect to the parameters Rf and Re with a scale factor close to 1, ii) calanchi and river basins are similar respect to the bifurcation and length ratios (λ=1), iii) for the investigated calanchi the Melton number assumes values less than that (0.694) corresponding to the river case and a scale ratio ranging from 0.52 and 0.78 can be used, iv) calanchi and river basins have similar mean relief ratio values (λ=1.13) and v) calanchi present active geomorphic processes and therefore fall in a more juvenile stage with respect to river basins. Copyright © 2017 Elsevier B.V. All rights reserved.

Pseudo-Random Number Generators

Science.gov (United States)

Howell, L. W.; Rheinfurth, M. H.

1984-01-01

Package features comprehensive selection of probabilistic distributions. Monte Carlo simulations resorted to whenever systems studied not amenable to deterministic analyses or when direct experimentation not feasible. Random numbers having certain specified distribution characteristic integral part of simulations. Package consists of collector of "pseudorandom" number generators for use in Monte Carlo simulations.

Random Numbers and Quantum Computers

Science.gov (United States)

McCartney, Mark; Glass, David

2002-01-01

The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…

Transitional boundary layer in low-Prandtl-number convection at high Rayleigh number

Science.gov (United States)

Schumacher, Joerg; Bandaru, Vinodh; Pandey, Ambrish; Scheel, Janet

2016-11-01

The boundary layer structure of the velocity and temperature fields in turbulent Rayleigh-Bénard flows in closed cylindrical cells of unit aspect ratio is revisited from a transitional and turbulent viscous boundary layer perspective. When the Rayleigh number is large enough the boundary layer dynamics at the bottom and top plates can be separated into an impact region of downwelling plumes, an ejection region of upwelling plumes and an interior region (away from side walls) that is dominated by a shear flow of varying orientation. This interior plate region is compared here to classical wall-bounded shear flows. The working fluid is liquid mercury or liquid gallium at a Prandtl number of Pr = 0 . 021 for a range of Rayleigh numbers of 3 ×105 Deutsche Forschungsgemeinschaft.

Analytic number theory

CERN Document Server

Iwaniec, Henryk

2004-01-01

Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results, many of which belong to the mainstream of arithmetic. One of the main attractions of analytic number theory is the vast diversity of concepts and methods it includes. The main goal of the book is to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, its beautiful theorems and powerful techniques. The book is written with graduate students in mind, and the authors tried to balance between clarity, completeness, and generality. The exercis

Heat transfer analysis for magnetohydrodynamics axisymmetric flow between stretching disks in the presence of viscous dissipation and Joule heating

Directory of Open Access Journals (Sweden)

N. Khan

2015-05-01

Full Text Available The investigation of heat transfer analysis on steady MHD axi-symmetric flow between two infinite stretching disks in the presence of viscous dissipation and Joule heating is basic objective of this paper. Attention has been focused to acquire the similarity solutions of the equations governing the flow and thermal fields. The transformed boundary value problem is solved analytically using homotopy analysis method. The series solutions are developed and the convergence of these solutions is explicitly discussed. The analytical expressions for fluid velocity, pressure and temperature are constructed and analyzed for various set of parameter values. The numerical values for skin friction coefficient and the Nusselt number are presented in tabular form. Particular attention is given to the variations of Prandtl and Eckert numbers. We examined that the dimensionless temperature field is enhanced when we increase the values of Eckert number and Prandtl number.

Fast integration using quasi-random numbers

International Nuclear Information System (INIS)

Bossert, J.; Feindt, M.; Kerzel, U.

2006-01-01

Quasi-random numbers are specially constructed series of numbers optimised to evenly sample a given s-dimensional volume. Using quasi-random numbers in numerical integration converges faster with a higher accuracy compared to the case of pseudo-random numbers. The basic properties of quasi-random numbers are introduced, various generators are discussed and the achieved gain is illustrated by examples

Fast integration using quasi-random numbers

Science.gov (United States)

Bossert, J.; Feindt, M.; Kerzel, U.

2006-04-01

Quasi-random numbers are specially constructed series of numbers optimised to evenly sample a given s-dimensional volume. Using quasi-random numbers in numerical integration converges faster with a higher accuracy compared to the case of pseudo-random numbers. The basic properties of quasi-random numbers are introduced, various generators are discussed and the achieved gain is illustrated by examples.

Analysis of surface roughness effects on heat transfer in micro-conduits

Energy Technology Data Exchange (ETDEWEB)

Koo, J.; Kleinstreuer, C. [North Carolina State University, Raleigh, NC (United States). Dept. of Mechanical and Aerospace Engineering

2005-06-01

Modern heat rejection systems, such as micro-heat sinks, are attractive because of their potential for high performance at small size and low weight. However, the impact of microscale effects on heat transfer have to be considered and quantitatively analyzed in order to gain physical insight and accurate Nusselt number data. The relative surface roughness (SR) was selected as a key microscale parameter, represented by a porous medium layer (PML) model. Assuming steady laminar fully developed liquid flow in microchannels and microtubes, the SR effects in terms of PML thermal conductivity ratio and Darcy number on the dimensionless temperature profile and Nusselt number were analyzed. In summary, the PML characteristics, especially the SR-number and conductivity ratio k{sub m}/k{sub f}, greatly affect the heat transfer performance where the Nusselt number can be either higher or lower than the conventional value. The PML influence is less pronounced in microtubes than in parallel-plate microchannels. (author)

Fibonacci number of the tadpole graph

Directory of Open Access Journals (Sweden)

Joe DeMaio

2014-10-01

Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.

The LHC in numbers

CERN Multimedia

Alizée Dauvergne

2010-01-01

What makes the LHC the biggest particle accelerator in the world? Here are some of the numbers that characterise the LHC, and their equivalents in terms that are easier for us to imagine.   Feature Number Equivalent Circumference ~ 27 km   Distance covered by beam in 10 hours ~ 10 billion km a round trip to Neptune Number of times a single proton travels around the ring each second 11 245   Speed of protons first entering the LHC 299 732 500 m/s 99.9998 % of the speed of light Speed of protons when they collide 299 789 760 m/s 99.9999991 % of the speed of light Collision temperature ~ 1016 °C ove...

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Numbers

Science.gov (United States)

Xiao, X.; Edwards, J. R.; Hassan, H. A.; Gaffney, R. L., Jr.

2007-01-01

A new turbulence model suited for calculating the turbulent Prandtl number as part of the solution is presented. The model is based on a set of two equations: one governing the variance of the enthalpy and the other governing its dissipation rate. These equations were derived from the exact energy equation and thus take into consideration compressibility and dissipation terms. The model is used to study two cases involving shock wave/boundary layer interaction at Mach 9.22 and Mach 5.0. In general, heat transfer prediction showed great improvement over traditional turbulence models where the turbulent Prandtl number is assumed constant. It is concluded that using a model that calculates the turbulent Prandtl number as part of the solution is the key to bridging the gap between theory and experiment for flows dominated by shock wave/boundary layer interactions.

Path-fan Ramsey numbers

NARCIS (Netherlands)

Salman, M.; Broersma, Haitze J.

2003-01-01

For two given graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the smallest positive integer $p$ such that for every graph $F$ on $p$ vertices the following holds: either $F$ contains $G$ as a subgraph or the complement of $F$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers

Path-fan Ramsey numbers

NARCIS (Netherlands)

Salman, M.; Broersma, Haitze J.

For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest positive integer $p$ such that for every graph $G$ on $p$ vertices the following holds: either $G$ contains $F$ as a subgraph or the complement of $G$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers

Path-kipas Ramsey numbers

NARCIS (Netherlands)

Salman, M.; Broersma, Haitze J.

2007-01-01

For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest positive integer $p$ such that for every graph $G$ on $p$ vertices the following holds: either $G$ contains $F$ as a subgraph or the complement of $G$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers

Unbounding the mental number line – New evidence on children’s spatial representation of numbers

Directory of Open Access Journals (Sweden)

Tanja eLink

2014-01-01

Full Text Available Number line estimation (i.e., indicating the position of a given number on a physical line is a standard assessment of children’s spatial representation of number magnitude. Importantly, there is an ongoing debate on the question in how far the bounded task version with start and endpoint given (e.g., 0 and 100 might induce specific estimation strategies and thus may not allow for unbiased inferences on the underlying representation. Recently, a new unbounded version of the task was suggested with only the start point and a unit fixed (e.g., the distance from 0 to 1. In adults this task provided a less biased index of the spatial representation of number magnitude. Yet, so far there are no children data available for the unbounded number line estimation task. Therefore, we conducted a cross-sectional study on primary school children performing both, the bounded and the unbounded version of the task. We observed clear evidence for systematic strategic influences (i.e., the consideration of reference points in the bounded number line estimation task for children older than grade two whereas there were no such indications for the unbounded version for any one of the age groups. In summary, the current data corroborate the unbounded number line estimation task to be a valuable tool for assessing children's spatial representation of number magnitude in a systematic and unbiased manner. Yet, similar results for the bounded and the unbounded version of the task for first- and second-graders may indicate that both versions of the task might assess the same underlying representation for relatively younger children - at least in number ranges familiar to the children assessed. This is of particular importance for inferences about the nature and development of children's magnitude representation.

Generation of Random Numbers and Parallel Random Number Streams for Monte Carlo Simulations

Directory of Open Access Journals (Sweden)

L. Yu. Barash

2012-01-01

Full Text Available Modern methods and libraries for high quality pseudorandom number generation and for generation of parallel random number streams for Monte Carlo simulations are considered. The probability equidistribution property and the parameters when the property holds at dimensions up to logarithm of mesh size are considered for Multiple Recursive Generators.

Number Meaning and Number Grammar in English and Spanish

Science.gov (United States)

Bock, Kathryn; Carreiras, Manuel; Meseguer, Enrique

2012-01-01

Grammatical agreement makes different demands on speakers of different languages. Being widespread in the languages of the world, the features of agreement systems offer valuable tests of how language affects deep-seated domains of human cognition and categorization. Number agreement is one such domain, with intriguing evidence that typological…

The magic of a number system

DEFF Research Database (Denmark)

Elmasry, Amr Ahmed Abd Elmoneim; Jensen, Claus; Katajainen, Jyrki

2010-01-01

We introduce a new number system that supports increments with a constant number of digit changes. We also give a simple method that extends any number system supporting increments to support decrements using the same number of digit changes. In the new number system the weight of the ith digit i...... is 2 i-1, and hence we can implement a priority queue as a forest of heap-ordered complete binary trees. The resulting data structure guarantees O(1) worst-case cost per insert and O(lg n) worst-case cost per delete, where n is the number of elements stored....

BKP and projective Hurwitz numbers

Science.gov (United States)

Natanzon, Sergey M.; Orlov, Aleksandr Yu.

2017-06-01

We consider d-fold branched coverings of the projective plane RP^2 and show that the hypergeometric tau function of the BKP hierarchy of Kac and van de Leur is the generating function for weighted sums of the related Hurwitz numbers. In particular, we get the RP^2 analogues of the CP^1 generating functions proposed by Okounkov and by Goulden and Jackson. Other examples are Hurwitz numbers weighted by the Hall-Littlewood and by the Macdonald polynomials. We also consider integrals of tau functions which generate Hurwitz numbers related to base surfaces with arbitrary Euler characteristics sc {e}, in particular projective Hurwitz numbers sc {e}=1.

Finite time exergy analysis and multi-objective ecological optimization of a regenerative Brayton cycle considering the impact of flow rate variations

International Nuclear Information System (INIS)

Naserian, Mohammad Mahdi; Farahat, Said; Sarhaddi, Faramarz

2015-01-01

Highlights: • Defining a dimensionless parameter includes the finite-time and size concepts. • Inserting the concept of exergy of fluid streams into finite-time thermodynamics. • Defining, drawing and modifying of maximum ecological function curve. • Suggesting the appropriate performance zone, according to maximum ecological curve. - Abstract: In this study, the optimal performance of a regenerative Brayton cycle is sought through power and then ecological function maximization using finite-time thermodynamic concept and finite-size components. Multi-objective optimization is used for maximizing the ecological function. Optimizations are performed using genetic algorithm. In order to take into account the finite-time and finite-size concepts in current problem, a dimensionless mass-flow parameter is introduced deploying time variations. The variations of output power, total exergy destruction of the system, and decision variables for the optimum state (maximum ecological function state) are compared to the maximum power state using the dimensionless parameter. The modified ecological function in optimum state is obtained and plotted relating to the dimensionless mass-flow parameter. One can see that the modified ecological function study results in a better performance than that obtained with the maximum power state. Finally, the appropriate performance zone of the heat engine will be obtained

The Congruent Number Problem

Indian Academy of Sciences (India)

One could endlessly churn out congruent numbers following the method in Box 1 without being certain when a given number n (or n x m 2, for some integer m) will ap- pear on the list. Continuing in this way ·would exhaust one's computing resources, not to mention one's patience! Also, this procedure is of no avail if n is not ...

MHD and radiation effects on moving isothermal vertical plate with variable mass diffusion

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2006-01-01

Full Text Available An analysis is performed to study the effects of thermal radiation on unsteady free convective flow over a moving vertical plate with mass transfer in the presence of magnetic field. The fluid considered here is a gray, absorbing-emitting radiation but a non- scattering medium. The plate temperature is raised to T 0 and the concentration level near the plate is also raised linearly with time. The dimensionless governing equations are solved using the Laplace transform technique. The velocity, temperature and concentration are studied for different parameters like the magnetic field parameter, radiation parameter, thermal Grashof number, mass Grashof number and time. It is observed that the velocity decreases with increasing magnetic field parameter or radiation parameter. .

Magnetohydrodynamic flow of generalized Maxwell fluids in a rectangular micropump under an AC electric field

Energy Technology Data Exchange (ETDEWEB)

Zhao, Guangpu [School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021 (China); Jian, Yongjun, E-mail: jianyj@imu.edu.cn [School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021 (China); Chang, Long [School of Mathematics and Statistics, Inner Mongolia University of Finance and Economics, Hohhot, Inner Mongolia 010051 (China); Buren, Mandula [School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021 (China)

2015-08-01

By using the method of separation of variables, an analytical solution for the magnetohydrodynamic (MHD) flow of the generalized Maxwell fluids under AC electric field through a two-dimensional rectangular micropump is reduced. By the numerical computation, the variations of velocity profiles with the electrical oscillating Reynolds number Re, the Hartmann number Ha, the dimensionless relaxation time De are studied graphically. Further, the comparison with available experimental data and relevant researches is presented. - Highlights: • MHD flow of the generalized Maxwell fluids under AC electric field is analyzed. • The MHD flow is confined to a two-dimensional rectangular micropump. • Analytical solution is obtained by using the method of separation of variables. • The influences of related parameters on the MHD velocity are discussed.

Effect of heat radiation in a Walter’s liquid B fluid over a stretching sheet with non-uniform heat source/sink and elastic deformation

Directory of Open Access Journals (Sweden)

A.K. Abdul Hakeem

2014-07-01

Full Text Available In this present article heat transfer in a Walter’s liquid B fluid over an impermeable stretching sheet with non-uniform heat source/sink, elastic deformation and radiation are reported. The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The dimensionless governing equations for this investigation are solved analytically using hyper geometric functions. The results are carried out for prescribed surface temperature (PST and prescribed power law surface heat flux (PHF. The effects of viscous dissipation, Prandtl number, Eckert number, heat source/sink parameter with elastic deformation and radiation are shown in the several plots and addressed.

Simulation on Natural Convection of a Nanofluid along an Isothermal Inclined Plate

Science.gov (United States)

Mitra, Asish

2017-08-01

A numerical algorithm is presented for studying laminar natural convection flow of a nanofluid along an isothermal inclined plate. By means of similarity transformation, the original nonlinear partial differential equations of flow are transformed to a set of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical analysis in Matlab environment. Dimensionless velocity, temperature profiles and nanoparticle concentration for various angles of inclination are illustrated graphically. The effects of Prandtl number, Brownian motion parameter and thermophoresis parameter on Nusselt number are also discussed. The results of the present simulation are then compared with previous one available in literature with good agreement.

Magnetohydrodynamic flow of generalized Maxwell fluids in a rectangular micropump under an AC electric field

International Nuclear Information System (INIS)

Zhao, Guangpu; Jian, Yongjun; Chang, Long; Buren, Mandula

2015-01-01

By using the method of separation of variables, an analytical solution for the magnetohydrodynamic (MHD) flow of the generalized Maxwell fluids under AC electric field through a two-dimensional rectangular micropump is reduced. By the numerical computation, the variations of velocity profiles with the electrical oscillating Reynolds number Re, the Hartmann number Ha, the dimensionless relaxation time De are studied graphically. Further, the comparison with available experimental data and relevant researches is presented. - Highlights: • MHD flow of the generalized Maxwell fluids under AC electric field is analyzed. • The MHD flow is confined to a two-dimensional rectangular micropump. • Analytical solution is obtained by using the method of separation of variables. • The influences of related parameters on the MHD velocity are discussed

Modelling aspects of two phase flow

International Nuclear Information System (INIS)

Mayinger, F.

1977-01-01

In two phase flow scaling is much more limited to very narrowly defined physical phenomena than in single phase fluids. For complex and combined phenomena it can be achieved not by using dimensionless numbers alone but in addition a detailed mathematical description of the physical problem - usually in the form of a computer program - must be available. An important role plays the scaling of the thermodynamic data of the modelling fluid. From a literature survey and from own scaling experiments the conclusion can be drawn that Freon is a quite suitable modelling fluid for scaling steam-water mixtures. However, whithout a theoretical description of the phenomena nondimensional numbers for scaling two phase flow must be handled very carefully. (orig.) [de

Theoretical study of chemical reaction effects on vertical oscillating plate with variable temperature

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2006-01-01

Full Text Available An exact solution to the flow of a viscous incompressible unsteady flow past an infinite vertical oscillating plate with variable temperature and mass diffusion is presented here, taking into account of the homogeneous chemical reaction of first-order. Both the plate temperature and the concentration level near the plate are raised linearly with respect to time. The dimensionless governing equations has been obtained by the Laplace transform method, when the plate is oscillating harmonically in its own plane. The effects of velocity and concentration are studied for different parameters like phase angle, chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time are studied. The solutions are valid only for small values of time t. It is observed that the velocity increases with decreasing phase angle ωt or chemical reaction parameter. .

Mass transfer effects on vertical oscillating plate with heat flux

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2007-01-01

Full Text Available Theoretical solution of unsteady viscous incompressible flow past an infinite vertical oscillating plate with uniform heat flux and mass diffusion is presented here, taking into account of the homogeneous chemical reaction of first-order. The temperature from the plate to the fluid at an uniform rate and the mass is diffused uniformly. The dimensionless governing equations has been obtained by the Laplace transform method, when the plate is oscillating harmonically in its own plane. The effects of velocity and concentration are studied for different parameters like phase angle chemical reaction parameter, thermal Grashof number, mass Grashof number Schmidt number and time are studied. The so­lutions are valid only for small values of time t. It is observed that the velocity increases with decreasing phase angle ωt or chemical reaction parameter.

The interaction of thermal radiation on vertical oscillating plate with variable temperature and mass diffusion

Directory of Open Access Journals (Sweden)

Muthucumaraswamy R.

2006-01-01

Full Text Available Thermal radiation effects on unsteady free convective flow of a viscous incompressible flow past an infinite vertical oscillating plate with variable temperature and mass diffusion has been studied. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The plate temperature is raised linearly with respect to time and the concentration level near the plate is also raised linearly with respect to time. An exact solution to the dimensionless governing equations has been obtained by the Laplace transform method, when the plate is oscillating harmonically in its own plane. The effects of velocity, temperature and concentration are studied for different parameters like phase angle, radiation parameter, Schmidt number, thermal Grashof number, mass Grashof number and time are studied. It is observed that the velocity increases with decreasing phase angle ωt. .

Natural convection heat and mass transfer in MHD fluid flow past a moving vertical plate with variable surface temperature and concentration in a porous medium

Directory of Open Access Journals (Sweden)

K. Javaherdeh

2015-09-01

Full Text Available A numerical investigation of two-dimensional steady laminar free convection flow with heat and mass transfer past a moving vertical plate in a porous medium subjected to a transverse magnetic field is carried out. The temperature and concentration level at the plate surface are assumed to follow a power-law type of distribution. The governing non-linear set of equations is solved numerically employing a fully implicit finite difference method. Results are presented to illustrate the influence of different parameters such as Grashof number (Gr, porosity parameter (Kp, magnetic field parameter (Mn and exponents in the power law variation of the surface temperature and concentration, m and n. The dimensionless velocity, temperature and concentration profiles are analyzed and numerical data for the local Nusselt number and Sherwood number are presented. The study accentuates the significance of the relevant parameters.

Viscous Flow over Nonlinearly Stretching Sheet with Effects of Viscous Dissipation

Directory of Open Access Journals (Sweden)

Javad Alinejad

2012-01-01

Full Text Available The flow and heat transfer characteristics of incompressible viscous flow over a nonlinearly stretching sheet with the presence of viscous dissipation is investigated numerically. The similarity transformation reduces the time-independent boundary layer equations for momentum and thermal energy into a set of coupled ordinary differential equations. The obtained equations, including nonlinear equation for the velocity field and differential equation by variable coefficient for the temperature field , are solved numerically by using the fourth order of Runge-Kutta integration scheme accompanied by shooting technique with Newton-Raphson iteration method. The effect of various values of Prandtl number, Eckert number and nonlinear stretching parameter are studied. The results presented graphically show some behaviors such as decrease in dimensionless temperature due to increase in Pr number, and curve relocations are observed when heat dissipation is considered.

Transfinite Numbers

Indian Academy of Sciences (India)

this is a characteristic difference between finite and infinite sets and created an immensely useful branch of mathematics based on this idea which had a great impact on the whole of mathe- matics. For example, the question of what is a number (finite or infinite) is almost a philosophical one. However Cantor's work turned it ...

Defense Horizons. Number 79, April 2015

Science.gov (United States)

2015-04-01

law , no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB...79, April 2015 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT...aggression. Even more issues emerged following the downing of Malaysian Airlines Flight 17 over Ukraine in July 2014, and cross-border ar- tillery renewed

Women In Numbers - Europe workshop

CERN Document Server

Bucur, Alina; Feigon, Brooke; Schneps, Leila

2015-01-01

Covering topics in graph theory, L-functions, p-adic geometry, Galois representations, elliptic fibrations, genus 3 curves and bad reduction, harmonic analysis, symplectic groups and mould combinatorics, this volume presents a collection of papers covering a wide swath of number theory emerging from the third iteration of the international Women in Numbers conference, “Women in Numbers - Europe” (WINE), held on October 14–18, 2013 at the CIRM-Luminy mathematical conference center in France. While containing contributions covering a wide range of cutting-edge topics in number theory, the volume emphasizes those concrete approaches that make it possible for graduate students and postdocs to begin work immediately on research problems even in highly complex subjects.

Digital random-number generator

Science.gov (United States)

Brocker, D. H.

1973-01-01

For binary digit array of N bits, use N noise sources to feed N nonlinear operators; each flip-flop in digit array is set by nonlinear operator to reflect whether amplitude of generator which feeds it is above or below mean value of generated noise. Fixed-point uniform distribution random number generation method can also be used to generate random numbers with other than uniform distribution.

Higher-order Nielsen numbers

Directory of Open Access Journals (Sweden)

Peter Saveliev

2005-04-01

Full Text Available Suppose X, Y are manifolds, f,g:X→Y are maps. The well-known coincidence problem studies the coincidence set C={x:f(x=g(x}. The number m=dim X−dim Y is called the codimension of the problem. More general is the preimage problem. For a map f:X→Z and a submanifold Y of Z, it studies the preimage set C={x:f(x∈Y}, and the codimension is m=dim X+dim Y−dim Z. In case of codimension 0, the classical Nielsen number N(f,Y is a lower estimate of the number of points in C changing under homotopies of f, and for an arbitrary codimension, of the number of components of C. We extend this theory to take into account other topological characteristics of C. The goal is to find a “lower estimate” of the bordism group Ωp(C of C. The answer is the Nielsen group Sp(f,Y defined as follows. In the classical definition, the Nielsen equivalence of points of C based on paths is replaced with an equivalence of singular submanifolds of C based on bordisms. We let Sp'(f,Y=Ωp(C/∼N, then the Nielsen group of order p is the part of Sp'(f,Y preserved under homotopies of f. The Nielsen number Np(F,Y of order p is the rank of this group (then N(f,Y=N0(f,Y. These numbers are new obstructions to removability of coincidences and preimages. Some examples and computations are provided.

An adventurer's guide to number theory

CERN Document Server

Friedberg, Richard

1995-01-01

In this delightful guide, a noted mathematician and teacher offers a witty, historically oriented introduction to number theory, dealing with properties of numbers and with numbers as abstract concepts. Written for readers with an understanding of arithmetic and beginning algebra, the book presents the classical discoveries of number theory, including the work of Pythagoras, Euclid, Diophantus, Fermat, Euler, Lagrange and Gauss.Unlike many authors, however, Mr. Friedberg encourages students to think about the imaginative, playful qualities of numbers as they consider such subjects as primes

Schmidt number for quantum operations

International Nuclear Information System (INIS)

Huang Siendong

2006-01-01

To understand how entangled states behave under local quantum operations is an open problem in quantum-information theory. The Jamiolkowski isomorphism provides a natural way to study this problem in terms of quantum states. We introduce the Schmidt number for quantum operations by this duality and clarify how the Schmidt number of a quantum state changes under a local quantum operation. Some characterizations of quantum operations with Schmidt number k are also provided

Certain number-theoretic episodes in algebra

CERN Document Server

Sivaramakrishnan, R

2006-01-01

Many basic ideas of algebra and number theory intertwine, making it ideal to explore both at the same time. Certain Number-Theoretic Episodes in Algebra focuses on some important aspects of interconnections between number theory and commutative algebra. Using a pedagogical approach, the author presents the conceptual foundations of commutative algebra arising from number theory. Self-contained, the book examines situations where explicit algebraic analogues of theorems of number theory are available. Coverage is divided into four parts, beginning with elements of number theory and algebra such as theorems of Euler, Fermat, and Lagrange, Euclidean domains, and finite groups. In the second part, the book details ordered fields, fields with valuation, and other algebraic structures. This is followed by a review of fundamentals of algebraic number theory in the third part. The final part explores links with ring theory, finite dimensional algebras, and the Goldbach problem.

Numerical Calculation of the Peaking Factor of a Water-Cooled W/Cu Monoblock for a Divertor

International Nuclear Information System (INIS)

Han Le; Chang Haiping; Zhang Jingyang; Xu Tiejun

2015-01-01

In order to accurately predict the incident critical heat flux (ICHF, the heat flux at the heated surface when CHF occurs) of a water-cooled W/Cu monoblock for a divertor, the exact knowledge of its peaking factors (f p ) under one-sided heating conditions with different design parameters is a key issue. In this paper, the heat conduction in the solid domain of a water-cooled W/Cu monoblock is calculated numerically by assuming the local heat transfer coefficients (HTC) of the cooling wall to be functions of the local wall temperature, so as to obtain f p . The reliability of the calculation method is validated by an experimental example result, with the maximum error of 2.1% only. The effects of geometric and flow parameters on the f p of a water-cooled W/Cu monoblock are investigated. Within the scope of this study, it is shown that the f p increases with increasing dimensionless W/Cu monoblock width and armour thickness (the shortest distance between the heated surface and Cu layer), and the maximum increases are 43.8% and 22.4% respectively. The dimensionless W/Cu monoblock height and Cu thickness have little effect on f p . The increase of Reynolds number and Jakob number causes the increase of f p , and the maximum increases are 6.8% and 9.6% respectively. Based on the calculated results, an empirical correlation on peaking factor is obtained via regression. These results provide a valuable reference for the thermal-hydraulic design of water-cooled divertors. (paper)

Spray characteristics and spray cooling heat transfer in the non-boiling regime

International Nuclear Information System (INIS)

Cheng, Wen-Long; Han, Feng-Yun; Liu, Qi-Nie; Fan, Han-Lin

2011-01-01

Spray cooling is an effective method for dissipating high heat fluxes in the field of electronics thermal control. In this study, experiments were performed with distilled water as a test liquid to study the spray cooling heat transfer in non-boiling regime. A Phase Doppler Anemometry (PDA) was used to study the spray characteristics. The effects of spray flow rate, spray height, and inlet temperature on spray cooling heat transfer were investigated. It was found that the parameters affect heat transfer of spray cooling in non-boiling regime by the spray characteristics and working fluid thermophysical properties. Then the corresponding droplet axial velocity and Sauter mean diameter (SMD) were successfully correlated with mean absolute error of 15%, which were based upon the orifice diameter, the Weber and Reynolds numbers of the orifice flow prior to liquid breakup, dimensionless spray height and spray cross-section radius. The heat transfer in non-boiling regime was correlated with a mean absolute error of 7%, which was mainly associated with the working fluid thermophysical properties, the Weber and Reynolds numbers hitting the heating surface, dimensionless heating surface temperature and diameter. -- Highlights: → The spray flow rate, spray height, and inlet temperature affect heat transfer of spray cooling in non-boiling regime by the spray characteristics and the working fluid thermophysical properties. → Then the corresponding droplet axial velocity and Sauer mean diameter (SMD) were successfully correlated with mean absolute error of 15%. → The heat transfer in non-boiling regime was correlated with a mean absolute error of 7%.

Comment on ‘On the units radian and cycle for the quantity plane angle’

Science.gov (United States)

Leonard, B. P.

2016-12-01

In the referenced paper, Ian Mills addresses the confusion caused by the treatment of plane angle in the International System of Units (SI). As he points out, what the SI calls an ‘angle’ is not a dimensional physical quantity but, rather, the dimensionless numerical value of the angle when expressed in radians, thus creating widespread confusion regarding terminology and notation. For example, Mills shows that for the harmonic oscillator, if the conventional argument of the sinusoid represents an angle, it must be divided by a dimensional constant equal to one radian in order to correctly render it dimensionless, thereby greatly clarifying the notation. However, there is a problem with the author’s interpretation of frequency. Although, for uniform rotation, Mills correctly defines the revolution frequency as the number of complete revolutions, N, divided by the time interval, he takes the unit for N to be ‘cycle’ (which he defines as one revolution) rather than the correct unit: the number one. The unit for ‘frequency’ then appears to be ‘cycle per second’ (i.e. revolution per second), whereas it should be one per second, correctly called hertz. Thus Mills concludes that ‘frequency’ is the same physical quantity as angular velocity and calls for the ‘hertz’ to be redefined as 2π rad s-1, a non-coherent derived unit for angular velocity. This misinterpretation of frequency corrupts the remainder of the author’s discussion of the examples considered. In my comment, I explain and correct these and related errors.

Numerical analysis of a heat-generating, truncated conical porous bed in a fluid-filled enclosure

International Nuclear Information System (INIS)

Chakravarty, Aranyak; Datta, Priyankan; Ghosh, Koushik; Sen, Swarnendu; Mukhopadhyay, Achintya

2016-01-01

Analysis of natural convection in enclosures containing heat generating porous medium has important applications related to geothermal, chemical, thermal and nuclear energy such as in-vessel cooling of debris beds in nuclear reactors, cooling of coal stockpiles etc. The objective of the present numerical study is to characterise the pattern of fluid flow and energy transfer during steady laminar natural convective flow in a cylindrical enclosure with a centrally placed heat generating porous bed. Flow through porous region is modelled using Darcy–Brinkmann–Forchheimer model and local thermal equilibrium is assumed for the porous region. Analysis is carried out for a wide range of Rayleigh number (Ra), Darcy number (Da) and thermal conductivity ratio, as well as for different bed geometries. It is observed that in addition to Ra and Da, the bed geometry also plays a very important role in determining flow field and temperature distribution within the enclosure. Interestingly, a significant change is observed in energy transfer mode from the porous bed corresponding to specific values of bed permeability and bed heat generation rate. This is characterised in terms of Ra and Da. Further, it is observed that this change in energy transfer mode is highly dependent on Ra. - Highlights: • Natural convection is analysed in an enclosure with a heat generating porous bed. • Effect of dimensionless parameters as well as bed geometry has been investigated. • Energy transfer mechanism from porous bed changes with dimensionless parameters. • Bed geometry significantly affects fluid flow and energy transfer in the enclosure.

Two Popular Books for Quantitative Literacy: What the Numbers Say, and The Numbers Game

Directory of Open Access Journals (Sweden)

Robert G. Root

2010-01-01

Full Text Available Niederman, Derrick, and Boyum, David. What the Numbers Say: A Field Guide to Mastering Our Numerical World. (New York: Broadway Books/Random House, 2003. 288 pp. Hardcover, ISBN 978-0-7679-0998-3. Paperback, 978-0-7679-0999-0. Available as an eBook.Blastland, Michael, and Dilnot, Andrew. The Numbers Game: The Commonsense Guide to Understanding Numbers in the News, in Politics and in Life. (New York: Gotham Books/Penguin, 2009. 192 pp. Hardcover, ISBN 978-1-5924-0423-0. Paperback, ISBN 978-1-5924-0485-8. Available as an eBook.Popular books on quantitative literacy need to be easy to read, reasonably comprehensive in scope, and include examples that are thought-provoking and memorable. In contrast to textbooks, popular books can dispense with exercises and structure, and instead offer an informal voice and an inviting style. In this genre John Allen Paulos’ Innumeracy is widely regarded as a classic. However, Paulos' book is out of date, and it takes a whimsical approach to many topics. The goal of this review is to acquaint the reader with two more recent entries into the genre. What the Numbers Say by Derrick Niederman and David Boyum takes an expansive view of quantitative literacy. The Numbers Game by Michael Blastland and Andrew Dilnot, on the other hand, focuses on reasoning surrounding statistics and uncertainty in contemporary society. The Numbers Game is a revised American edition of The Tiger That Isn’t, which grew out of a BBC radio program, More or Less.

Quality pseudo-random number generator

International Nuclear Information System (INIS)

Tarasiuk, J.

1996-01-01

The pseudo-random number generator (RNG) was written to match needs of nuclear and high-energy physics computation which in some cases require very long and independent random number sequences. In this random number generator the repetition period is about 10 36 what should be sufficient for all computers in the world. In this article the test results of RNG correlation, speed and identity of computations for PC, Sun4 and VAX computer tests are presented

Number Theory and Applications : Proceedings of the International Conferences on Number Theory and Cryptography

CERN Document Server

Ramakrishnan, B

2009-01-01

This collection of articles contains the proceedings of the two international conferences (on Number Theory and Cryptography) held at the Harish - Chandra Research Institute. In recent years the interest in number theory has increased due to its applications in areas like error-correcting codes and cryptography. These proceedings contain papers in various areas of number theory, such as combinatorial, algebraic, analytic and transcendental aspects, arithmetic algebraic geometry, as well as graph theory and cryptography. While some papers do contain new results, several of the papers are expository articles that mention open questions, which will be useful to young researchers.

The european emergency number 112 - the questionnaire

Directory of Open Access Journals (Sweden)

Krzysztof Goniewicz

2017-07-01

Conclusions. Most of the respondents (92% identify the 112 number as an emergency number that allows them to connect to emergency services from anywhere in the European Union. A significant number of respondents (47% identify the 112 number as an emergency number in Poland. One in three respondents will use the 999 number to contact the emergency services as a witness to an emergency in Poland. Non-medical university students more often (63% will use the 112 emergency number than medical college students (41%. Respondents (98% confirmed the usefulness of a unified emergency number throughout Europe, but decided that they were not sufficiently informed about 112 as the European emergency number.

Vegetable oil and fat viscosity forecast models based on iodine number and saponification number

International Nuclear Information System (INIS)

Toscano, G.; Riva, G.; Foppa Pedretti, E.; Duca, D.

2012-01-01

Vegetable oil and fats can be considered as an important renewable source for the energy production. There are many applications where these biofuels are used directly in engines. However, the use of pure vegetable oils causes some problems as consequence of its chemical and physical characteristic. Viscosity is one of the most important parameters affecting several physical and mechanical processes of the operation of the engine. The determination of this parameter at different tis important to determine the behavior of the vegetable oil and fats. In this work we investigated the effects of two analytical chemical parameters (iodine number and saponification number) and forecasting models have been proposed. -- Highlights: ► Vegetable oil and fat viscosity is predicted by mathematical model based on saponification number and iodine number. ► Unsaturated vegetable oils with small size molecules of fatty acids have a lower viscosity values. ► The models proposed show an average error lower than 12%

General Approach for Composite Thermoelectric Systems with Thermal Coupling: The Case of a Dual Thermoelectric Cooler

Directory of Open Access Journals (Sweden)

Cuautli Yanehowi Flores-Niño

2015-06-01

Full Text Available In this work, we show a general approach for inhomogeneous composite thermoelectric systems, and as an illustrative case, we consider a dual thermoelectric cooler. This composite cooler consists of two thermoelectric modules (TEMs connected thermally in parallel and electrically in series. Each TEM has different thermoelectric (TE properties, namely thermal conductance, electrical resistance and the Seebeck coefficient. The system is coupled by thermal conductances to heat reservoirs. The proposed approach consists of derivation of the dimensionless thermoelectric properties for the whole system. Thus, we obtain an equivalent figure of merit whose impact and meaning is discussed. We make use of dimensionless equations to study the impact of the thermal conductance matching on the cooling capacity and the coefficient of the performance of the system. The equivalent thermoelectric properties derived with our formalism include the external conductances and all intrinsic thermoelectric properties of each component of the system. Our proposed approach permits us changing the thermoelectric parameters of the TEMs and the working conditions of the composite system. Furthermore, our analysis shows the effect of the number of thermocouples on the system. These considerations are very useful for the design of thermoelectric composite systems. We reproduce the qualitative behavior of a commercial composite TEM connected electrically in series.

Internal Electric Field In The Space Charge Layer Of A Solar Cell Based On Silicon In The Presence Of Excitons

Directory of Open Access Journals (Sweden)

Modou Faye

2015-08-01

Full Text Available Abstract The author faced with the impossibility of assessing the relative importance of the different contributions of physical quantities appearing in the equations of transport he appealed to the dimensional analysis. Thus by grouping the physical parameters the dependent and independent variables it generates dimensionless numbers. The latter having a physical significance make it possible to characterize the various contributions. To solve the dimensionless equations obtained strongly coupled reduced scale the author opts for a numerical method. The spatial discretization variable pitch and tight at the interfaces of different zones of the field because of the strong gradients in these regions is adopted. The equations are then integrated in the numerical domain using the finite volume method and the coefficients are approached by the schema of the power Patankar law. The resulting system of algebraic equations is solved by the method of double course combined with an iterative relaxation line by line type Gauss-Seidel. Furthermore with a volumetric coefficient of coupling which depends on the dissociation of the excitons and the average temperature field the author has studied the influence of some physical parameters on the total density of photocurrent such that the heating factor the conversion velocity and the volume coupling coefficient of charge carriers.

Fibonacci and Catalan Numbers An Introduction

CERN Document Server

Grimaldi, Ralph

2012-01-01

In this one-of-a-kind book, Ralph Grimaldi uses his extensive experience from the classroom and as a leader of mini-courses to present an accessible, single resource on the topics of Fibonacci Numbers and Catalan Numbers . The book first embarks on a complete treatment of Fibonacci numbers. Starting with a historical background on the topic, the author goes on to present the properties of Fibonacci numbers, a slew of introductory-level examples, and in-depth discussion of related topics including compositions and palindromes; tiling and Fibonacci numbers

Advanced number theory with applications

CERN Document Server

Mollin, Richard A

2009-01-01

Algebraic Number Theory and Quadratic Fields Algebraic Number Fields The Gaussian Field Euclidean Quadratic Fields Applications of Unique Factorization Ideals The Arithmetic of Ideals in Quadratic Fields Dedekind Domains Application to Factoring Binary Quadratic Forms Basics Composition and the Form Class Group Applications via Ambiguity Genus Representation Equivalence Modulo p Diophantine Approximation Algebraic and Transcendental Numbers Transcendence Minkowski's Convex Body Theorem Arithmetic Functions The Euler-Maclaurin Summation Formula Average Orders The Riemann zeta-functionIntroduction to p-Adic AnalysisSolving Modulo pn Introduction to Valuations Non-Archimedean vs. Archimedean Valuations Representation of p-Adic NumbersDirichlet: Characters, Density, and Primes in Progression Dirichlet Characters Dirichlet's L-Function and Theorem Dirichlet DensityApplications to Diophantine Equations Lucas-Lehmer Theory Generalized Ramanujan-Nagell Equations Bachet's Equation The Fermat Equation Catalan and the A...

Essays on the theory of numbers

CERN Document Server

Dedekind, Richard

1963-01-01

Two classic essays by great German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, the other is an attempt to give the logical basis for transfinite numbers and properties of the natural numbers.

A new definition of Bejan number

Directory of Open Access Journals (Sweden)

Awad Mohamed M.

2012-01-01

Full Text Available A new definition of Bejan number will be generated by replacing the thermal diffusivity with the mass diffusivity. For example, the Schmidt number is the mass transfer analog of the Prandtl number. For the case of Reynolds analogy (Sc = Pr = = 1, both current and new definitions of Bejan number are the same. This new definition is useful and needed for diffusion of mass (mass diffusion.

Study of dimensionless quantities to analyse front and rear wall of ...

Indian Academy of Sciences (India)

hydrodynamic quantities describe the mechanism behind flow pattern present in .... beam is focused into a small spot adjustable approximately 0.1 to 0.8 mm in ... moves, the liquefied metal around the 'keyhole' flows back in, solidifying and.

Choose Wisely: Static or Kinetic Friction--The Power of Dimensionless Plots

Science.gov (United States)

Ludwigsen, Daniel; Svinarich, Kathryn

2009-01-01

Consider a problem of sliding blocks, one stacked atop the other, resting on a frictionless table. If the bottom block is pulled horizontally, nature makes a choice: if the applied force is small, static friction between the blocks accelerates the blocks together, but with a large force the blocks slide apart. In that case, kinetic friction still…

Effect of buoyancy on fuel containment in an open-cycle gas-core nuclear rocket engine.

Science.gov (United States)

Putre, H. A.

1971-01-01

Analysis aimed at determining the scaling laws for the buoyancy effect on fuel containment in an open-cycle gas-core nuclear rocket engine, so conducted that experimental conditions can be related to engine conditions. The fuel volume fraction in a short coaxial flow cavity is calculated with a programmed numerical solution of the steady Navier-Stokes equations for isothermal, variable density fluid mixing. A dimensionless parameter B, called the Buoyancy number, was found to correlate the fuel volume fraction for large accelerations and various density ratios. This parameter has the value B = 0 for zero acceleration, and B = 350 for typical engine conditions.

Tests of three tapered airfoils based on the N.A.C.A. 2200, the N.A.C.A.-M6, and the Clark Y sections

Science.gov (United States)

Anderson, Raymond F

1934-01-01

Three tapered airfoils based on the N.A.C.A. 2200, the N.A.C.A.-M6, and the Clark Y sections were tested in the variable-density wind tunnel at a Reynolds Number of approximately 3,100,000. The models, which were of aspect ratio 6, had constant core center sections and rounded tips, and tapered in thickness from 18 percent at the roots to 9 percent at the tips. The aerodynamic characteristics are given by the usual dimensionless coefficients plotted for both positive and negative angles of attack and by effective profile-drag coefficients plotted against lift coefficients.

Magnetohydrodynamic Three-Dimensional Flowof a Second-Grade Fluid with Heat Transfer

Science.gov (United States)

Hayat, Tasawar; Nawaz, Muhammad

2010-09-01

An analysis has been carried out for the heat transfer on steady boundary layer flow of a secondgrade fluid bounded by a stretching sheet. The magnetohydrodynamic nature of the fluid is considered in the presence of Hall and ion-slip currents. The nonlinear mathematical problem is computed by a powerful tool, namely, the homotopy analysis method (HAM). A comparative study between the present and existing limiting results is carefully made. Convergence regarding the obtained solution is discussed. Skin friction coefficients and Nusselt number are analyzed. Effects of embedded parameters on the dimensionless velocities and temperature are examined

Experimental investigation of shock wave diffraction over a single- or double-sphere model

Science.gov (United States)

Zhang, L. T.; Wang, T. H.; Hao, L. N.; Huang, B. Q.; Chen, W. J.; Shi, H. H.

2017-01-01

In this study, the unsteady drag produced by the interaction of a shock wave with a single- and a double-sphere model is measured using imbedded accelerometers. The shock wave is generated in a horizontal circular shock tube with an inner diameter of 200 mm. The effect of the shock Mach number and the dimensionless distance between spheres is investigated. The time-history of the drag coefficient is obtained based on Fast Fourier Transformation (FFT) band-block filtering and polynomial fitting of the measured acceleration. The measured peak values of the drag coefficient, with the associated uncertainty, are reported.

Parametric numerical investigaion of natural convection in a heat-generating fluid with phase transitions

Energy Technology Data Exchange (ETDEWEB)

Aksenova, A.E.; Chudanov, V.V.; Strizhov, V.F.; Vabishchevich, P.N. [Institute of Nuclear Safety Russian Academy Science, Moscow (Russian Federation)

1995-09-01

Unsteady natural convection of a heat-generating fluid with phase transitions in the enclosures of a square section with isothermal rigid walls is investigated numerically for a wide range of dimensionless parameters. The quasisteady state solutions of conjugate heat and mass transfer problem are compared with available experimental results. Correlation relations for heat flux distributions at the domain boundaries depending on Rayleigh and Ostrogradskii numbers are obtained. It is shown that generally heat transfer is governed both by natural circulation and crust formation phenomena. Results of this paper may be used for analysis of experiments with prototypic core materials.

Radiative mixed convection over an isothermal cone embedded in a porous medium with variable permeability

KAUST Repository

El-Amin, Mohamed; Ebrahiem, N.A.; Salama, Amgad; Sun, S.

2011-01-01

The interaction of mixed convection with thermal radiation of an optical dense viscous fluid adjacent to an isothermal cone imbedded in a porous medium with Rosseland diffusion approximation incorporating the variation of permeability and thermal conductivity is numerically investigated. The transformed conservation laws are solved numerically for the case of variable surface temperature conditions. Numerical results are given for the dimensionless temperature profiles and the local Nusselt number for various values of the mixed convection parameter , the cone angle parameter ?, the radiation-conduction parameter R d, and the surface temperature parameter H. Copyright 2011 M. F. El-Amin et al.

High temperature thermoelectric energy conversion

International Nuclear Information System (INIS)

Wood, C.

1986-01-01

Considerable advances were made in the late '50's and early early '60's in the theory and development of materials for high-temperature thermoelectric energy conversion. This early work culminated in a variety of materials, spanning a range of temperatures, with the product of the figure of merit, Z, and temperature, T, i.e., the dimensionless figure of merit, ZT, of the order of one. This experimental limitation appeared to be universal and led a number of investigators to explore the possibility that a ZT - also represents a theoretical limitation. It was found not to be so

Random numbers spring from alpha decay

International Nuclear Information System (INIS)

Frigerio, N.A.; Sanathanan, L.P.; Morley, M.; Clark, N.A.; Tyler, S.A.

1980-05-01

Congruential random number generators, which are widely used in Monte Carlo simulations, are deficient in that the number they generate are concentrated in a relatively small number of hyperplanes. While this deficiency may not be a limitation in small Monte Carlo studies involving a few variables, it introduces a significant bias in large simulations requiring high resolution. This bias was recognized and assessed during preparations for an accident analysis study of nuclear power plants. This report describes a random number device based on the radioactive decay of alpha particles from a 235 U source in a high-resolution gas proportional counter. The signals were fed to a 4096-channel analyzer and for each channel the frequency of signals registered in a 20,000-microsecond interval was recorded. The parity bits of these frequency counts (0 for an even count and 1 for an odd count) were then assembled in sequence to form 31-bit binary random numbers and transcribed to a magnetic tape. This cycle was repeated as many times as were necessary to create 3 million random numbers. The frequency distribution of counts from the present device conforms to the Brockwell-Moyal distribution, which takes into account the dead time of the counter (both the dead time and decay constant of the underlying Poisson process were estimated). Analysis of the count data and tests of randomness on a sample set of the 31-bit binary numbers indicate that this random number device is a highly reliable source of truly random numbers. Its use is, therefore, recommended in Monte Carlo simulations for which the congruential pseudorandom number generators are found to be inadequate. 6 figures, 5 tables

Asymptotics of quantum weighted Hurwitz numbers

Science.gov (United States)

Harnad, J.; Ortmann, Janosch

2018-06-01

This work concerns both the semiclassical and zero temperature asymptotics of quantum weighted double Hurwitz numbers. The partition function for quantum weighted double Hurwitz numbers can be interpreted in terms of the energy distribution of a quantum Bose gas with vanishing fugacity. We compute the leading semiclassical term of the partition function for three versions of the quantum weighted Hurwitz numbers, as well as lower order semiclassical corrections. The classical limit is shown to reproduce the simple single and double Hurwitz numbers studied by Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74). The KP-Toda τ-function that serves as generating function for the quantum Hurwitz numbers is shown to have the τ-function of Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74) as its leading term in the classical limit, and, with suitable scaling, the same holds for the partition function, the weights and expectations of Hurwitz numbers. We also compute the zero temperature limit of the partition function and quantum weighted Hurwitz numbers. The KP or Toda τ-function serving as generating function for the quantum Hurwitz numbers are shown to give the one for Belyi curves in the zero temperature limit and, with suitable scaling, the same holds true for the partition function, the weights and the expectations of Hurwitz numbers.

The precision of mapping between number words and the approximate number system predicts children's formal math abilities.

Science.gov (United States)

Libertus, Melissa E; Odic, Darko; Feigenson, Lisa; Halberda, Justin

2016-10-01

Children can represent number in at least two ways: by using their non-verbal, intuitive approximate number system (ANS) and by using words and symbols to count and represent numbers exactly. Furthermore, by the time they are 5years old, children can map between the ANS and number words, as evidenced by their ability to verbally estimate numbers of items without counting. How does the quality of the mapping between approximate and exact numbers relate to children's math abilities? The role of the ANS-number word mapping in math competence remains controversial for at least two reasons. First, previous work has not examined the relation between verbal estimation and distinct subtypes of math abilities. Second, previous work has not addressed how distinct components of verbal estimation-mapping accuracy and variability-might each relate to math performance. Here, we addressed these gaps by measuring individual differences in ANS precision, verbal number estimation, and formal and informal math abilities in 5- to 7-year-old children. We found that verbal estimation variability, but not estimation accuracy, predicted formal math abilities, even when controlling for age, expressive vocabulary, and ANS precision, and that it mediated the link between ANS precision and overall math ability. These findings suggest that variability in the ANS-number word mapping may be especially important for formal math abilities. Copyright © 2016 Elsevier Inc. All rights reserved.

Phase diagram of a polarized Fermi gas across a Feshbach resonance in a potential trap

International Nuclear Information System (INIS)

Yi, W.; Duan, L.-M.

2006-01-01

We map out the detailed phase diagram of a trapped ultracold Fermi gas with population imbalance across a wide Feshbach resonance. We show that under the local density approximation, the properties of the atoms in any (anisotropic) harmonic traps are universally characterized by three dimensionless parameters: the normalized temperature, the dimensionless interaction strength, and the population imbalance. We then discuss the possible quantum phases in the trap, and quantitatively characterize their phase boundaries in various typical parameter regions

The natural number bias and its role in rational number understanding in children with dyscalculia. Delay or deficit?

Science.gov (United States)

Van Hoof, Jo; Verschaffel, Lieven; Ghesquière, Pol; Van Dooren, Wim

2017-12-01

Previous research indicated that in several cases learners' errors on rational number tasks can be attributed to learners' tendency to (wrongly) apply natural number properties. There exists a large body of literature both on learners' struggle with understanding the rational number system and on the role of the natural number bias in this struggle. However, little is known about this phenomenon in learners with dyscalculia. We investigated the rational number understanding of learners with dyscalculia and compared it with the rational number understanding of learners without dyscalculia. Three groups of learners were included: sixth graders with dyscalculia, a chronological age match group, and an ability match group. The results showed that the rational number understanding of learners with dyscalculia is significantly lower than that of typically developing peers, but not significantly different from younger learners, even after statistically controlling for mathematics achievement. Next to a delay in their mathematics achievement, learners with dyscalculia seem to have an extra delay in their rational number understanding, compared with peers. This is especially the case in those rational number tasks where one has to inhibit natural number knowledge to come to the right answer. Copyright © 2017 Elsevier Ltd. All rights reserved.

Characterization of rarefaction waves in van der Waals fluids

Science.gov (United States)

Yuen, Albert; Barnard, John J.

2015-12-01

We calculate the isentropic evolution of an instantaneously heated foil, assuming a van der Waals equation of state with the Maxwell construction. The analysis by Yuen and Barnard [Phys. Rev. E 92, 033019 (2015), 10.1103/PhysRevE.92.033019] is extended for the particular case of three degrees of freedom. We assume heating to temperatures in the vicinity of the critical point. The self-similar profiles of the rarefaction waves describing the evolution of the foil display plateaus in density and temperature due to a phase transition from the single-phase to the two-phase regime. The hydrodynamic equations are expressed in a dimensionless form and the solutions form a set of universal curves, depending on a single parameter: the dimensionless initial entropy. We characterize the rarefaction waves by calculating how the plateau length, density, pressure, temperature, velocity, internal energy, and sound speed vary with dimensionless initial entropy.

Hyperreal Numbers for Infinite Divergent Series

OpenAIRE

Bartlett, Jonathan

2018-01-01

Treating divergent series properly has been an ongoing issue in mathematics. However, many of the problems in divergent series stem from the fact that divergent series were discovered prior to having a number system which could handle them. The infinities that resulted from divergent series led to contradictions within the real number system, but these contradictions are largely alleviated with the hyperreal number system. Hyperreal numbers provide a framework for dealing with divergent serie...

Lepton number violation in theories with a large number of standard model copies

International Nuclear Information System (INIS)

Kovalenko, Sergey; Schmidt, Ivan; Paes, Heinrich

2011-01-01

We examine lepton number violation (LNV) in theories with a saturated black hole bound on a large number of species. Such theories have been advocated recently as a possible solution to the hierarchy problem and an explanation of the smallness of neutrino masses. On the other hand, the violation of the lepton number can be a potential phenomenological problem of this N-copy extension of the standard model as due to the low quantum gravity scale black holes may induce TeV scale LNV operators generating unacceptably large rates of LNV processes. We show, however, that this issue can be avoided by introducing a spontaneously broken U 1(B-L) . Then, due to the existence of a specific compensation mechanism between contributions of different Majorana neutrino states, LNV processes in the standard model copy become extremely suppressed with rates far beyond experimental reach.

Practical scaling law for photoelectron angular distributions

International Nuclear Information System (INIS)